Frobenius can be Ferdinand Georg Frobenius 1849 1917 , mathematician Frobenius algebra Frobenius endomorphism Frobenius inner product Frobenius norm Frobenius method Frobenius group Frobenius theorem differential topology Frobenius Orgelbyggeri , Danish organ building firm Georg Ludwig Frobenius 1566 1645 , German publisher Johann Froben Johannes Frobenius 1460 1527 , publisher and printer in Basel Hieronymus Froben Hieronymus Frobenius 1501 1563 , publisher and printer in Basel, son of Johannes Ambrosius Frobenius 1537 1602 , publisher and printer in Basel, son of Hieronymus Leo Frobenius 1873 1938 , ethnographer Nikolaj Frobenius b. 1965 , Norwegian writer and screenwriter August Sigmund Frobenius 1741 , German chemist disambig Category Surnames es Frobenius fr Frobenius ja ru ... more details
There are several mathematical theorems named after Ferdinand Georg Frobenius . They include Frobenius theorem differential topology Frobenius theorem in differential geometry and topology for integrable subbundles Frobenius theorem real division algebras Frobenius theorem in abstract algebra characterizing the finite dimensional real division algebras Frobenius reciprocity theorem in group representation theory describing the reciprocity relation between restricted and induced representations on a subgroup Perron Frobenius theorem in matrix theory concerning the eigenvalue s and eigenvector s of a matrix with positive real coefficients. disambig Category Mathematical disambiguation de Satz von Frobenius ja pl Twierdzenie Frobeniusa ... more details
In number theory , a Frobenius pseudoprime is a composite number which passes a three step probable prime test set out by Jon Grantham in section 3 of his paper Frobenius pseudoprimes . ref Jon Grantham. http www.pseudoprime.com pseudo1.pdf Frobenius pseudoprimes . Mathematics of Computation , 70 234 873 891. 2001. ref Although a single round of Frobenius is slower than a single round of most standard tests, it has the advantage of a much smaller worst case per round error bound of 1 7710, which would require 7 rounds to achieve with the Miller Rabin primality test according to best known bounds. Strong Frobenius pseudoprimes A strong Frobenius pseudoprime is a pseudoprime which obeys an additional restriction beyond that required for a Frobenius pseudoprime. ref MathWorld title Strong Frobenius pseudoprime urlname StrongFrobeniusPseudoprime ref See also Pseudoprime Ferdinand Georg Frobenius References references External links http www.mathpages.com home kmath003 kmath003.htm Symmetric Pseudoprimes at MathPages Category Pseudoprimes Category Article Feedback 5 Numtheory stub ... more details
Notability Astro date February 2012 Infobox planet minorplanet yes width 25em bgcolour FFFFC0 apsis name Frobenius symbol image caption discovery yes discovery ref discoverer P. G. Comba discovery site Prescott Observatory Prescott discovered March 8, 1997 designations yes mp name 22474 alt names 1997 ED8 named after Ferdinand Georg Frobenius mp category orbit ref epoch May 14, 2008 aphelion 3.0095689 perihelion 2.1661471 semimajor eccentricity 0.1629575 period 1520.5793306 avg speed inclination 3.58292 asc node 6.08330 mean anomaly 250.62819 arg peri 157.96105 satellites physical characteristics yes dimensions mass density surface grav escape velocity sidereal day axial tilt pole ecliptic lat pole ecliptic lon albedo temperatures temp name1 mean temp 1 max temp 1 temp name2 max temp 2 spectral type abs magnitude 15.7 22474 Frobenius 1997 ED8 is a Asteroid belt main belt asteroid discovered on March 8, 1997 by P. G. Comba at Prescott Observatory Prescott . References Reflist External links http ssd.jpl.nasa.gov sbdb.cgi?sstr 22474 Frobenius JPL Small Body Database Browser on 22474 Frobenius DEFAULTSORT Frobenius Category Main Belt asteroids Category Astronomical objects discovered in 1997 beltasteroid stub de 22474 Frobenius fa it 22474 Frobenius pl 22474 Frobenius pt 22474 Frobenius uk 22474 vi 22474 Frobenius yo 22474 Frobenius ... more details
Infobox scientist name Leo Frobenius image Leo Frobenius.jpg image size 150px caption Leo Frobenius birth ... prizes religion footnotes signature Leo Viktor Frobenius 29 June 1873 9 August 1938 was an ethnologist ... museum . In 1897 1898 Frobenius defined several culture areas Kulturkreise , cultures showing similar traits that have been spread by diffusion or invasion. With his term paideuma , Frobenius wanted ... as a living organism was influenced by the theories of Oswald Spengler . Frobenius taught at the University ... the Frobenius Institute in his honour in 1946. His writings with Douglas Fox were a channel through ... to Gassire s lute , an epic from West Africa which Frobenius had encountered in Mali . Ezra Pound corresponded with Frobenius from the 1920s, initially on economic topics. The story made its way into Pound s Cantos through this connection. In the 1930s, Frobenius claimed that he had found proof of the existence of the lost continent of Atlantis . ref Leo Frobenius , Encyclop dia Britannica , 1960 edition ref Due to his studies in African history , Frobenius is a figure of renown in many ... of N gritude , who once claimed that Frobenius had given Africa back its dignity and identity. Aim C saire also quoted Frobenius as praising African people as being civilized to the marrow of their bones ... Soyinka , in his 1986 Nobel Lecture, criticized Frobenius for his schizophrenic view of Yoruba ... laureates 1986 soyinka lecture.html ref Quoting Frobenius s statement that I was moved to silent melancholy ... Afrikas Z rich 1933 Notes references External links Commons category Leo Frobenius http www.frobenius institut.de Homepage of the Frobenius Institute http www.independent.co.uk opinion commentators ... Metadata see Wikipedia Persondata . NAME Frobenius, Leo ALTERNATIVE NAMES SHORT DESCRIPTION DATE OF BIRTH 29 June 1873 PLACE OF BIRTH Berlin DATE OF DEATH 9 August 1938 PLACE OF DEATH DEFAULTSORT Frobenius ... archaeologists az L Fr b nius ca Leo Frobenius cs Leo Frobenius de Leo Frobenius es Leo Frobenius ... more details
Ambrosius Froben or in Latin Frobenius 1537 1602 was a Basel printer, and publisher of an almost complete Hebrew Talmud , 1578 1580. ref The way Jews lived five hundred years of printed words and images p51 Constance Harris 2009 Froben s grandson, Ambrosius, published an important Talmud, 1578 1580, under the supervision of the Jewish editor ref He was son of Hieronymus Frobenius 1501 65 , and grandson of Johann Froben 1460 1527 the Swiss scholar and printer. References reflist Persondata Metadata see Wikipedia Persondata . NAME Frobenius, Ambrosius ALTERNATIVE NAMES SHORT DESCRIPTION Swiss book publisher DATE OF BIRTH 1537 PLACE OF BIRTH DATE OF DEATH 1602 PLACE OF DEATH DEFAULTSORT Frobenius, Ambrosius Category Swiss book publishers people Category 1537 births Category 1602 deaths als Ambrosius Frobenius de Ambrosius Frobenius ... more details
In mathematics , a Frobenius group is a group action Types of actions transitive permutation group on a finite ... fixes a point. They are named after Ferdinand Georg Frobenius F. G. Frobenius . Structure The subgroup H of a Frobenius group G fixing a point of the set X is called the Frobenius complement . The identity ... the Frobenius kernel K . This is a theorem due to Frobenius. The Frobenius group G is the semidirect product of K and H math G K rtimes H math . Both the Frobenius kernel and the Frobenius complement ... year 1960 proved that the Frobenius kernel K is a nilpotent group . If H has even order then K is abelian. The Frobenius complement H has the property that every subgroup whose order is the product ... this means it is the extension of two cyclic groups. If a Frobenius complement H is not solvable then Hans ..., if a Frobenius complement coincides with its derived subgroup, then it is isomorphic with SL 2,5 . If a Frobenius complement H is solvable then it has a normal metacyclic subgroup such that the quotient is a subgroup of the symmetric group on 4 points. A finite group is a Frobenius complement ... s Notes, Principal Theorem IV, p38 The Frobenius kernel K is uniquely determined by G as it is the Fitting subgroup , and the Frobenius complement is uniquely determined up to conjugacy by the Schur Zassenhaus theorem . In particular a finite group G is a Frobenius group in at most one way. Examples ... on 3 points, with 6 elements. The Frobenius kernel K has order 3, and the complement H has order 2. For every ... s math x mapsto ax b math , math a ne 0 math acting naturally on F sub q sub is a Frobenius group ... of the Frobenius automorphism x x of F sub 8 sub and to be multiplication by any element not in the Characteristic ... Applications cyclic multiplicative group of F sub 8 sub . This Frobenius group acts Group action ... with marked points. The dihedral group of order 2 n with n odd is a Frobenius group with complement ..., then the semidirect product K.H is a Frobenius group. Many further examples can be generated ... more details
Image AarhusDom Orgel 1.jpg thumb right The Frobenius organ in Aarhus Cathedral Image Organ Pipes in J rlunde church.jpg thumb right Inside the Frobenius organ in J rlunde church Frobenius is a Denmark Danish firm of pipe organ organ builders. History Frobenius Orgelbyggeri Th. Frobenius & Sons Th. Frobenius & S nner Orgelbyggeri A S was founded in Copenhagen by Theodor Frobenius 1885 1972 in 1909. The firm moved to Lyngby in 1925. Theodor s sons Walther and Erik joined the company in 1944, at the same time that they began to build organs in the classical tradition, with tracker action mechanical action s and slider windchest s. They build organs with characteristic modern casework, usually arranging the pipework of each manual such that three to six repeating arrangements of front pipes are shown in the fa ade. Their organ development after 1925 was in the best tradition of neoclassicism neo classical design. Notable Frobenius organs Aarhus Cathedral , Denmark, 89 stops 1928 2001 The largest church organ in Denmark ref cite web url http www.denstoredanske.dk Danmarks geografi og historie Danmarks geografi Jylland Jylland byer rhus rhus Arkitektur og museer. title Aarhus arkitektur og museer author Den Store Danske Encyklop di language Danish accessdate 26 March 2012 ref The Queen s College, Oxford , 22 stops 1965 Church of the Assumption, Tullamore, Ireland, 53 stops 1965 relocated ... of the Canongate Canongate Kirk, Edinburgh, Scotland , 19 stops 1998 The 1000th organ built by Frobenius ... author Magle, Frederik accessdate 26 March 2012 ref Sources Guy Oldham Ole Olesen Frobenius , Grove Music Online ed. L. Macy Accessed 2007 06 25 , http www.grovemusic.com N. Friis Th. Frobenius & Co 1909 1959 Kongens Lyngby, 1959 P.J. Basch Frobenius to the Americas , in Music the AGO and RCCO Magazine ... Frobenius Orgelbyggeri de Frobenius Orgelbyggeri fr Frobenius Orgelbyggeri no TH. Frobenius og S nner Orgelbyggeri sv TH. Frobenius og S nner Orgelbyggeri A S ... more details
A Frobenius matrix is a special kind of square matrix from numerical mathematics . A matrix is a Frobenius matrix if it has the following three properties all entries on the main diagonal are ones the entries below the main diagonal of at most one column are arbitrary every other entry is zero The following matrix is an example. math A begin pmatrix 1 & 0 & 0 & cdots & 0 0 & 1 & 0 & cdots & 0 0 & a 32 & 1 & cdots & 0 vdots & vdots & vdots & ddots & vdots 0 & a n2 & 0 & cdots & 1 end pmatrix math Frobenius matrices are Invertible matrix invertible . The inverse of a Frobenius matrix is again a Frobenius matrix, equal to the original matrix with changed signs outside the main diagonal. The inverse of the example above is therefore math A 1 begin pmatrix 1 & 0 & 0 & cdots & 0 0 & 1 & 0 & cdots & 0 0 & a 32 & 1 & cdots & 0 vdots & vdots & vdots & ddots & vdots 0 & a n2 & 0 & cdots & 1 end pmatrix math Frobenius matrices are named after Ferdinand Georg Frobenius . An alternative name for this class of matrices is Gauss transformation , after Carl Friedrich Gauss ref Golub and Van Loan, p. 95. ref . They are used in the process of Gaussian elimination to represent the Gaussian transformations. If a matrix is multiplied from the left left multiplied with a Frobenius matrix, a linear combination of the remaining rows is added to a particular row of the matrix. Multiplication with the inverse matrix subtracts the corresponding linear combination from the given row. This corresponds to one of the elementary operations of Gaussian elimination besides the operation of transposing the rows and multiplying a row with a scalar multiple . Notes references References Gene H. Golub and Charles F. Van Loan 1996 . Matrix Computations , third edition, Johns Hopkins University Press. ISBN 0 8018 5413 X hardback , ISBN 0 8018 5414 8 paperback . Translation Ref de Frobeniusmatrix oldid 21677532 Category Matrices Linear algebra stub de Frobeniusmatrix nl Frobenius matrix pl Posta Frobeniusa ... more details
dablink Frobenius algebra is also an archaic name for the group ring of a finite group In mathematics , especially in the fields of representation theory and module theory , a Frobenius algebra is a dimension ... form which gives the algebras particularly nice duality theories. Frobenius algebras began ... Ferdinand Georg FrobeniusFrobenius . Tadashi Nakayama mathematician Nakayama discovered the beginnings ... . Jean Dieudonn Dieudonn used this to characterize Frobenius algebras in his harv Dieudonn 1958 where he called this property of Frobenius algebras a perfect duality . Frobenius algebras were generalized to quasi Frobenius ring s, those Noetherian ring s whose right regular representation is injective module injective . In recent times, interest has been renewed in Frobenius algebras due to connections ... algebra A defined over a field mathematics field k is said to be a Frobenius algebra if A is equipped ... equation a b , c a , b c . This bilinear form is called the Frobenius form of the algebra. Equivalently ... no nonzero left ideal ring theory ideal of A . A Frobenius algebra is called symmetric if ... matrix algebra defined over a field k is a Frobenius algebra with Frobenius form a , b tr a b where ... of a Frobenius algebra. Every group ring of a finite group over a field is a Frobenius algebra, with Frobenius form a , b the coefficient of the identity element in a b . This is a special ... sup is a Frobenius algebra in the sense of the second example. For a field k not of characteristic 2, the three dimensional k algebra k x , y x , y sup 2 sup is not a Frobenius algebra in the sense of the second example. Properties The product of rings direct product and tensor product of Frobenius algebras are Frobenius algebras. A finite dimensional commutative ring commutative local ring local algebra over a field is Frobenius if and only if the right regular module is injective, if and only if the algebra has a unique minimal ideal . Commutative, local Frobenius algebras are precisely the Krull ... more details
The Frobenius Institute originally Forschungsinstitut fur Kulturmorphologie is Germany s oldest anthropology anthropological research institute. Founded in 1925, it is named after Leo Frobenius . The institution is located at Gruneburgplatz 1 in Frankfurt am Main . An autonomous organization, it is associated with the Johann Wolfgang Goethe University , and works in collaboration with two other organizations, the Institut f r Ethnologie, and the Museum der Weltkulturen . ref name frobenius institut.de cite web url http www.frobenius institut.de index.php?option com content&task view&id 25&lang en title FROBENIUS INSTITUT an der Johann Wolfgang Goethe Universitat work frobenius institut.de accessdate 8 May 2011 ref It carries out ethnological and historical research. ref name deutsche kultur international.de cite web url http www.deutsche kultur international.de en org organisations frobenius institut ev an der johann wolfgang goethe universitaet zu frankfurt am main fi.html title Frobenius Institute at the Johann Wolfgang Goethe University, Frankfurt am Main publisher Deutsche Kulture International accessdate 8 May 2011 ref Originally established in Munich and known as the Forschungsinstitut fur Kulturmorphologie, it was renamed by Adolf Ellegard Jensen , its director after the 1938 death of Frobenius. ref name Gaillard2004 cite book last Gaillard first G rald title The Routledge dictionary of anthropologists url http books.google.com books?id vDad ohjPFwC&pg PA218 accessdate 8 May 2011 year 2004 publisher Psychology Press isbn 9780415228251 pages 218 ref References Reflist Category Research institutes in Germany Category Anthropological research institutes Category Organizations established in 1925 Category Education in Frankfurt ... more details
In mathematics, a Frobenius splitting , introduced by harvs txt author1 link Vikram Bhagvandas Mehta last Mehta last2 Ramanthan author2 link Annamalai Ramanathan year 1985 , is a splitting of the injective morphism O sub X sub F sub sub O sub X sub from a structure sheaf O sub X sub of a characteristic p 0 variety X to its image F sub sub O sub X sub under the Frobenius endomorphism F sub sub . The concept is named after Ferdinand Georg Frobenius . harvtxt Brion Kumar 2005 give a detailed discussion of Frobenius splittings. A fundamental property of Frobenius split projective scheme s X is that the higher cohomology H sup i sup X , L i 0 of ample line bundle s L vanishes. References Citation last1 Brion first1 Michel last2 Kumar first2 Shrawan title Frobenius splitting methods in geometry and representation theory publisher Birkh user Boston location Boston, MA series Progress in Mathematics isbn 978 0 8176 4191 7 doi 10.1007 b137486 mr 2107324 year 2005 volume 231 Citation last1 Mehta first1 V. B. last2 Ramanathan first2 A. title Frobenius splitting and cohomology vanishing for Schubert varieties doi 10.2307 1971368 mr 799251 year 1985 journal Annals of Mathematics Annals of Mathematics. Second Series issn 0003 486X volume 122 issue 1 pages 27 40 External links http sites.google.com site frobeniussplitting Conference on Frobenius splitting in algebraic geometry, commutative algebra, and representation theory at Michigan, 2010. Category Algebraic geometry ... more details
Nikolaj Frobenius born September 29, 1965 is a Norway Norwegian novelist and screen writer . File Frobenius.png thumb Frobenius was born in Oslo , but grew up at Rykkinn . He studied film writing and research at LCP, London. He has written several books and screenplays, including the screenplay for the classic Nordic film thriller Insomnia 1997 film Insomnia , which was adapted into a major Hollywood production in 2002. His international breakthrough as a novelist came with the novel Latours katalog 1996 . His books have been translated into eighteen languages, including English, French, Spanish, Italian, German, Russian and Danish. His novels have received critical acclaim both in Norway and internationally, and he has won several literary prizes for his writing. Nikolaj Frobenius is a former editor of the periodical Vinduet and worked as a commissioning editor for Norsk filmfond from 2005 2008. Frobenius has written several successful screenplays, including Dragonfly 2001 film Dragonfly 2001 . In 2011 he adapted his own novel, the semi autobiograhical Teori og praksis into the film S nner av Norge Sons of Norway . He lives and writes in Oslo. Bibliography Virvl 1986, poems Den unge Villiam Oxenstiernes lysende kj rlighet 1989 Helvetesfabel 1991 Latours katalog Insomnia 1997, screenplay Den sjenerte pornografen Dragonfly 2001 film Dragonfly screenplay, with Marius Holst 2001 Andre steder 2001 Det aller minste 2003 Teori og praksis 2004 En folkefiende screen play re adaption, 2005 Herlige nederlag artikler og intervjuer om litteratur og film 2007 Jeg skal vise dere frykten 2008 ... nm0296154 Nikolaj Frobenius on imdb.com Persondata NAME Frobenius, Nikolaj ALTERNATIVE NAMES SHORT ... Frobenius, Nikolaj Category 1965 births Category Living people Category Norwegian novelists Category Norwegian screenwriters Category People from B rum Norway writer stub cs Nikolaj Frobenius da Nikolaj Frobenius fr Nikolaj Frobenius no Nikolaj Frobenius ru , ... more details
In commutative algebra and field theory mathematics field theory , the Frobenius endomorphism after Ferdinand Georg Frobenius is a special endomorphism of commutative Ring mathematics rings with prime ... . The Frobenius endomorphism F is defined by F r r sup p sup for all r in R . Clearly this respects ... is F sub p sub T T sup p sup , where F T 0, but T 0. Fixed points of the Frobenius endomorphism Say R is an integral domain . The Frobenius map fixes all the elements of R which satisfy the equation ... the fixed point set of F is the prime field . Iterating the Frobenius map gives us a sequence of elements ... to the example above. The iterates of the Frobenius map are also used in defining the Frobenius closure and tight closure of an ideal. Frobenius for finite fields Let F sub q sub be the finite field ... 2 sup , the second iterate of Frobenius, fixes p sup 2 sup elements, so it will fix F sub p sup 2 ... group of any extension of finite fields. Frobenius for schemes Using the setup above, it is easy to extend the Frobenius map to the context of schemes. Let X be a scheme over a field k of characteristic ... . This forces R to be a characteristic p ring, so we can define the Frobenius endomorphism F for R ... of X , called the absolute Frobenius map . However, F is not necessarily an endomorphism of k schemes ... is lost. To preserve the properties of the k scheme X , one then introduces the relative Frobenius math X to X p math which is obtained by base change of X by math F k to k math . Frobenius for local ... will treat these cases separately for clarity. The definition of the Frobenius for finite fields can ... field s, there is a concept of Frobenius endomorphism which induces the Frobenius endomorphism in the corresponding ... may define the Frobenius map for elements of the ring of integers O sub L sub of L as an automorphism math s Phi math of L such that math s Phi x equiv x q mod Phi. math Frobenius for global fields In algebraic number theory , Frobenius elements are defined for extensions L K of global field s that are finite ... more details
In the mathematical field of differential geometry , a Frobenius manifold is a flat Riemannian manifold with a certain compatible multiplicative structure on the tangent space . The concept generalizes the notion of Frobenius algebra to tangent bundles. They were introduced by Dubrovin. ref B. Dubrovin Geometry of 2D topological eld theories. In Springer LNM, 1620 1996 , pp. 120 348. ref Frobenius manifolds occur naturally in the subject of symplectic topology , more specifically quantum cohomology . The broadest definition is in the category of Riemannian supermanifold s. We will limit the discussion here to smooth real manifolds. A restriction to complex manifolds is also possible. Definition Let M be a smooth manifold. An affine flat structure on M is a Sheaf mathematics sheaf T sup f sup of vector spaces that pointwisely span TM the tangent bundle and the tangent bracket of pairs of its sections vanishes. As a local example consider the coordinate vectorfields over a chart of M . A manifold admits an affine flat structure if one can glue together such vectorfields for a covering family of charts. Let further be given a Riemannian metric g on M . It is compatible to the flat structure if g X , Y is locally constant for all flat vector fields X and Y . A Riemannian manifold admits a compatible affine flat structure if and only if its curvature tensor vanishes everywhere ... that a linear Frobenius manifold M , g , with constant product is a Frobenius ... g A X,Y ,Z X Y Z Phi , math for all flat vector fields X , Y , and Z . A Frobenius ... Verlinde WDVV equation. Examples Beside Frobenius algebras, examples arise from quantum cohomology ... form g < , > is a complex Frobenius manifold. References Reflist 2. Yu.I. Manin, S.A. Merkulov http arxiv.org abs alg geom 9702014 Semisimple Frobenius super manifolds and quantum cohomology ... Frobenius Manifold Category Symplectic topology Category Riemannian manifolds Category Article ... more details
In matrix theory , the Frobenius covariants of a square matrix A are matrices A sub i sub associated with the eigenvalue, eigenvector and eigenspace eigenvalues and eigenvectors of A . ref name horn Roger A. Horn and Charles R. Johnson 1991 , Topics in Matrix Analysis . Cambridge University Press, ISBN 9780521467131 ref Each covariant is a projection linear algebra projection OF WHAT? on the eigenvalue, eigenvector and eigenspace eigenspace associated with sub i sub . Frobenius covariants are the coefficients of Sylvester s formula , that expresses a matrix function function of a matrix f A as a linear combination of its values on the eigenvalues of A . They are named after the mathematician Ferdinand Georg Frobenius Ferdinand Frobenius . Formal definition Let A be a diagonalizable matrix with k distinct eigenvalues, sub 1 sub , &hellip , sub k sub . The Frobenius covariant A sub i sub , for i 1,&hellip , k , is the matrix math A i prod j 1 atop j ne i k frac 1 lambda i lambda j A lambda j I . math Computing the covariants The Frobenius covariants of a matrix A can be obtained from any eigendecomposition A SDS sup 1 sup , where S is non singular and D is diagonal with D sub i , i sub sub i sub . If A has no multiple eigenvalues, then let c sub i sub be the i th left eigenvector of A , that is, the i th column of S and let r sub i sub be the i th right eigenvector of A , namely the i th row of S sup 1 sup . Then A sub i sub c sub i sub r sub i sub . If A has multiple eigenvalues then A sub i sub sub j sub c sub j sub r sub j sub , where the sum is over all rows and columns associated with the eigenvalue sub i sub . ref name horn rp p.521 Example Consider the two by two matrix math A begin bmatrix 1 & 3 4 & 2 end bmatrix . math This matrix has two eigenvalues, 5 and 2. The corresponding eigen decomposition is math A begin bmatrix 3 & 1 7 4 & 1 7 end bmatrix begin ... . math Hence the Frobenius covariants are math begin align A 1 & c 1 r 1 begin bmatrix 3 4 end bmatrix ... more details
Frobenius Forster 30 August 1709, at K nigsfeld, Bavaria K nigsfeld in Upper Bavaria 11 October 1791, at Ratisbon was a German Benedictine , Prince Abbot of St. Emmeram . Life After studying the humanities and philosophy at Freising and Ingolstadt , he entered the Benedictine monastery of St. Emmeram at Ratisbon where he took vows on 8 December 1728. He made his theological studies partly at his monastery and partly at Rott , where the Bavarian Benedictines had their common study house. Shortly after his elevation to the priesthood, in 1733, he became professor of philosophy and theology at St. Emmeram and for some time held the office of master of novices. In 1745 he was sent to the Benedictine university at Salzburg to teach philosophy and physics. Two years later he returned to his monastery where he taught philosophy and Holy Scriptures until he became librarian and prior in 1750. He had gained a reputation as a philosopher and scientist, and was one of the first religious who endeavoured to reconcile Scholastic philosophy with the Cartesianism Cartesian and the Leibniz Wolffian school . Though leaning towards the Leibniz Wolffian philosophy, he rejected many of its teachings, such as the cosmological optimism of Leibniz and the mechanism of Wolff, and was rather an eclectic than a slavish follower of any one system. In 1759 Forster was chosen one of the first members of the newly founded Bavarian Academy of Sciences . A year later he laid down the office of prior and was appointed provost at Hohengebraching , a dependency of St. Emmeram, situated about five miles south of Ratisbon. On 24 July 1762, he was elected as successor to the deceased Prince Abbot Johann Baptist Kraus of St. Emmeram. Forster s election was the inauguration of the golden era of St. Emmeram. The learned ... wstitle Frobenius Forster The entry cites ENDRES, Frobenius Forster in Strassburger theol. Studien ... German abbots Category 1791 deaths Category German Benedictines de Frobenius Forster ... more details
In mathematics , the Frobenius method , named after Ferdinand Georg Frobenius , is a way to find an infinite series solution for a second order ordinary differential equation of the form math z 2u p z zu q z u 0 , math with math u equiv d u over d z math pad 1em and pad 1em math u equiv d 2 u over d z 2 math in the vicinity of the regular singular point z 0 . We can divide by z sup 2 sup to obtain a differential equation of the form math u p z over z u q z over z 2 u 0 math which will not be solvable with regular power series solution of differential equations power series method s if either p z z or q z z sup 2 sup are not Analytic function analytic at z 0. The Frobenius method enables us to create a power series solution to such a differential equation, provided that p z and q z are themselves analytic at 0 or, being analytic elsewhere, both their limits at 0 exist and are finite . Explanation The Frobenius method tells us that we can seek a power series solution of the form math u z sum k 0 infty A kz k r , qquad A 0 neq 0 math Differentiating math u z sum k 0 infty k r A kz k r 1 math math u z sum k 0 infty k r 1 k r A kz k r 2 math Substituting math begin align & quad z 2 sum k 0 infty k r 1 k r A kz k r 2 zp z sum k 0 infty k r A kz k r 1 q z sum k 0 infty A kz k r & sum k 0 infty k r 1 k r A kz k r p z sum k 0 infty k r A kz k r q z sum k 0 infty A kz k r & sum k 0 infty k r 1 k r A kz k r p z k r A kz k r q z A kz k r & sum k 0 infty k r 1 k r p z k r ... only gave one solution to the given differential equation. In general, the Frobenius method gives ... External links mathworld urlname FrobeniusMethod title Frobenius Method John H. Mathews, http math.fullerton.edu mathews n2003 FrobeniusSeriesMod.html Module for Frobenius Series Solution cite ... proofs. Category Ordinary differential equations de Frobenius Methode ko it Metodo di Frobenius nl Methode van Frobenius km pt M todo de Frobenius th ... more details
Infobox scientist name Ferdinand Georg Frobenius image GeorgFrobenius.jpg image size 150px caption Ferdinand Georg Frobenius birth date birth date 1849 10 26 birth place Charlottenburg death date death ... equations br Group theory br Cayley&ndash Hamilton theorem br Frobenius method influences influenced awards Ferdinand Georg Frobenius October 26, 1849 August 3, 1917 was a Germans German mathematician ... Georg Frobenius was born on October 26, 1849 in Charlottenburg , a suburb of Berlin ref cite web ... ref from parents Christian Ferdinand Frobenius, a Protestant parson, and Christine Elizabeth ... Bio Frobenius was only in Berlin a year before he went to Z rich to take up an appointment as an ordinary ..., Frobenius worked in Z rich. It was there that he married, brought up his family, and did much ... died and, therefore, his chair in Berlin became vacant. Weierstrass, strongly believing that Frobenius ... to have Frobenius appointed. In 1893 he returned to Berlin, where he was elected to the Prussian Academy of Sciences . Contributions to group theory Group theory was one of Frobenius principal ... Sylow theorem on the existence of Sylow groups is one of those frequently used today. Frobenius ... of Character theory Frobenius reciprocity and the definition of what are now called Frobenius group s. A group G is said to be a Frobenius group if there is a subgroup H G such that math ... first paper about characters 1896 , Frobenius constructed the character table of the group math PSL ... of the symmetric and alternating groups . Contributions to number theory Frobenius introduced a canonical ... group is canonically associated to p . This is called the Frobenius conjugacy class of p and any element of the conjugacy class is called a Frobenius element of p . If we take for K the m th ... classes become elements , then for p not dividing m the Frobenius class in the Galois group is p mod m . From this point of view, the distribution of Frobenius conjugacy classes in Galois ... more details
In ring theory , the class of Frobenius rings and their generalizations are the extension of work done on Frobenius algebra s. Perhaps the most important generalization is that of quasi Frobenius rings QF rings , which are in turn generalized by right pseudo Frobenius rings PF rings and right finitely pseudo Frobenius rings FPF rings . Other diverse generalizations of quasi Frobenius rings include ... Frobenius . A partial list of pioneers in quasi Frobenius rings includes Richard Brauer R. Brauer ... to define quasi Frobenius rings first. In the following characterizations of each type of ring, many properties of the ring will be revealed. A ring R is quasi Frobenius if and only if R satisfies .... A Frobenius ring R is one satisfying any of the following equivalent conditions. Let J J R be the Jacobson radical of R . R is quasi Frobenius and the socle math mathrm soc R R cong R J math as right R modules. R is quasi Frobenius and math mathrm soc R R cong R J math as left R modules. As right ... R J math . For a commutative ring R , the following are equivalent R is Frobenius R is QF R is a finite ... of zero dimensional Gorenstein ring Gorenstein local rings . A ring R is right pseudo Frobenius ... of R . R is a cogenerator of Mod R and is a left Kasch ring. A ring R is right finitely pseudo Frobenius ... 2. Examples Every Frobenius k algebra is a Frobenius ring. Every semisimple ring is clearly quasi Frobenius, since all modules are projective and injective. Even more is true however semisimple rings are all Frobenius. This is easily verified by the definition, since for semisimple rings math ... serial rings are all Frobenius, and in fact have the additional property that every quotient ring R I is also Frobenius. It turns out that among commutative Artinian rings, the serial rings are exactly the rings whose nonzero quotients are all Frobenius. Many exotic PF and FPF rings can be found as examples in harv Faith 1984 See also Quasi Frobenius Lie algebra Notes The definitions for QF, PF ... more details
In mathematics , the Frobenius endomorphism is defined in any commutative ring R that has characteristic algebra characteristic p , where p is a prime number . Namely, the mapping that takes r in R to r sup p sup is a ring endomorphism of R . The image of is then R sup p sup , the subring of R consisting of p th powers. In some important cases, for example finite field s, is surjective . Otherwise is an endomorphism but not a ring automorphism . The terminology of geometric Frobenius arises by applying the spectrum of a ring construction to . This gives a mapping Spec R sup p sup Spec R of affine scheme s. Even in cases where R sup p sup R this is not the identity, unless R is the prime field . Mappings created by fibre product with , i.e. Grothendieck s relative point of view base change s, tend in scheme theory to be called geometric Frobenius . The reason for a careful terminology is that the Frobenius automorphism in Galois group s, or defined by transport of structure , is often the inverse mapping of the geometric Frobenius. As in the case of a cyclic group in which a generator is also the inverse of a generator, there are in many situations two possible definitions of Frobenius, and without a consistent convention some problem of a minus sign may appear. References Citation last1 Freitag first1 Eberhard last2 Kiehl first2 Reinhardt title tale cohomology and the Weil conjecture publisher Springer Verlag location Berlin, New York series Ergebnisse der Mathematik und ihrer Grenzgebiete 3 Results in Mathematics and Related Areas 3 isbn 978 3 540 12175 6 mr 926276 year 1988 volume 13 , p. 5 DEFAULTSORT Arithmetic And Geometric Frobenius Category Mathematical terminology Category Algebraic geometry Category Algebraic number theory ... more details
August Sigmund Frobenius 1727 first mentioned 1741? , Royal Society FRS ref name RS http www2.royalsociety.org DServe dserve.exe?dsqIni Dserve.ini&dsqApp Archive&dsqCmd Show.tcl&dsqDb Persons&dsqPos 0&dsqSearch 28 28text 29 3D 27frobenius 27 29 Royal Society Selected Fellows details ref , also known as Sigismond Augustus Frobenius , Joannes Sigismundus Augustus Frobenius , and Johann Sigismund August Froben , was a German born chemist in the 18th century who is known for the first detailed description of the properties of diethyl ether and the naming of this substance Spiritus Vini thereus . Not much is known about his life. He has worked in Paris, Germany, and Italy ref name Phil.Trans.1741 cite journal author C. Mortimer year 1741 title Abstracts of the Original Papers Communicated to the Royal Society by Sigismond Augustus Frobenius, M. D. concerning His Spiritus Vini Aethereus Collected by C. Mortimer, M. D. Secr. R. S. journal Phil. Trans. volume 41 issue 461 pages 864 870 pmid doi 10.1098 rstl.1739.0161 url http rstl.royalsocietypublishing.org content 41 452 461 864.full.pdf html ref . In the laboratory or Ambrose Godfrey in London he produced ether, following a method of Isaac Newton . His first article about ether was published 1730 in the Philosophical Transactions of the Royal Society under the title An Account of a Spiritus Vini thereus, Together with Several Experiments Tried ref name Phil.Trans.1730 cite journal author Dr. Frobenius year 1730 title An Account of a Spiritus Vini thereus, Together with Several Experiments Tried journal Phil. Trans. volume 36 issue ... . See also Diethyl ether External links wikisource de ADB Frobenius, August Sigmund Frobenius, August ... yes&andorexactfulltext and&x 0&y 0 Articles authored by Frobenius in the Philosophical Transactions of the Royal Society References references DEFAULTSORT Frobenius,August Sigmund Category German chemists Category Fellows of the Royal Society es August Sigmund Frobenius ... more details
In mathematics, the Frobenius determinant theorem is a discovery made in 1896 by the mathematician Richard Dedekind , who wrote a letter to Ferdinand Georg Frobenius F. G. Frobenius about it reproduced in harv Dedekind 1968 , with an English translation in harv Curtis 2003 loc p.51 . If one takes the multiplication table of a Group mathematics group G and replaces each entry g with the variable x sub g sub , and subsequently takes the determinant , then the determinant factors as a product of n irreducible polynomials, where n is the number of conjugacy classes. Moreover, each polynomial is raised to a power equal to its degree. Frobenius proved this surprising fact, and this theorem became known as the Frobenius determinant theorem. Formal statement Let a finite group math G math have elements math g 1, g 2, dots,g n math , and let math x g i math be associated with each element of math G math . Define the matrix math X G math with entries math a ij x g i g j math . Then math det X G prod j 1 r P j x g 1 ,x g 2 , dots,x g n deg P j math where r is the number of conjugacy classes of G . References Citation last1 Curtis first1 Charles W. authorlink Charles W. Curtis title Pioneers of Representation Theory Frobenius, Burnside, Schur, and Brauer url http books.google.com books?isbn 0821826778 publisher American Mathematical Society location Providence, R.I. series History of Mathematics isbn 978 0 8218 2677 5 doi 10.1090 S0273 0979 00 00867 3 mr 1715145 year 2003 http www.ams.org journals bull 2000 37 03 S0273 0979 00 00867 3 Review Citation last1 Dedekind first1 Richard author1 link Richard Dedekind editor1 last Fricke editor1 first Robert editor2 last Noether editor2 first Emmy editor2 link Emmy Noether editor3 last Ore editor3 first ystein title Gesammelte mathematische Werke. B nde I III origyear 1931 publisher Chelsea Publishing Co. location New York mr 0237282 ... Theory . Citation last1 Frobenius first1 Ferdinand Georg author1 link Ferdinand Georg Frobenius ... more details
In mathematics , a quasi Frobenius Lie algebra math mathfrak g , , , ,, , , , , beta math over a field math k math is a Lie algebra math mathfrak g , , , ,, , , , math equipped with a nondegenerate skew symmetric bilinear form math beta mathfrak g times mathfrak g to k math , which is a Lie algebra 2 cocycle of math mathfrak g math with values in math k math . In other words, math beta left left X,Y right ,Z right beta left left Z,X right ,Y right beta left left Y,Z right ,X right 0 math for all math X math , math Y math , math Z math in math mathfrak g math . If math beta math is a coboundary, which means that there exists a linear form math f mathfrak g to k math such that math beta X,Y f left X,Y right , math then math mathfrak g , , , ,, , , , , beta math is called a Frobenius Lie algebra . Equivalence with pre Lie algebras with nondegenerate invariant skew symmetric bilinear form If math mathfrak g , , , ,, , , , , beta math is a quasi Frobenius Lie algebra, one can define on math mathfrak g math another bilinear product math triangleleft math by the formula math beta left left X,Y right ,Z right beta left Z triangleleft Y,X right math . Then one has math left X,Y right X triangleleft Y Y triangleleft X math and math mathfrak g , triangleleft math is a pre Lie algebra . See also Lie coalgebra Lie bialgebra Lie algebra cohomology Frobenius algebra Quasi Frobenius ring References Jacobson, Nathan, Lie algebras , Republication of the 1962 original. Dover Publications, Inc., New York, 1979. ISBN 0 486 63832 4 Vyjayanthi Chari and Andrew Pressley, A Guide to Quantum Groups , 1994 , Cambridge University Press, Cambridge ISBN 0 521 55884 0. Category Lie algebras Category Coalgebras Category Symplectic topology ... more details
In mathematics , Frobenius theorem gives necessary and sufficient condition s for finding a maximal set ... math nabla u 1, nabla u 2, dots, nabla u n r math are linearly independent . The Frobenius ... of the Frobenius theorem is to form linear combinations among the operators L sub i sub so that the resulting ... to one correspondence with arbitrary functions of one variable. Frobenius theorem allows one ... of integration is known, then the corresponding solution is also known. Explain this better. Frobenius theorem in modern language The Frobenius theorem can be restated more economically in modern language. Frobenius original version of the theorem was stated in terms of Pfaffian system s, which ... or involutive if and only if it arises from a regular foliation . In this context, the Frobenius theorem ... the foliation is defined only on chart topology charts . Given the above definitions, Frobenius theorem ... algebra rank r , the rank being constant in value over U . The Frobenius theorem states that F ... follows from the close relationship between differential form s and Lie derivative s. Frobenius .... Consequently, the Frobenius theorem takes on the equivalent form that I D is closed under ... on U such that u x sub 0 sub y sub 0 sub . The conditions of the Frobenius theorem depend on whether ... . Banach manifolds The infinite dimensional version of the Frobenius theorem also holds on Banach ... Verlag year 1995 isbn 978 0 387 94338 1 pages Chapter VI The theorem of Frobenius nopp true ref ... of TN with &phi sup 1 sup E . The Frobenius theorem states that a subbundle E is integrable if and only ... versions of the Frobenius theorem. In particular, the fact that it has been stated for domains ... K hler theorem . History Despite being named for Ferdinand Georg Frobenius , the theorem was first ... conditions for the theorem, and Clebsch developed the necessary conditions. Frobenius is responsible .... Math. 20 1840 340 350. Frobenius, G. ber das Pfaffsche probleme , J. f r Reine und Agnew. Math. , 82 ... more details
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