for the journal Matrix Biology journal Merge to Matrix biology date May 2010 Matrix biology is the study of the structure and function of the extracellular matrix ECM and its interactions with proximal Cell biology cells . Matrix biologists usually do both basic research into structure and cellular interactions of the ECM and applied research into how these parameters are altered in disease or other pathological states. Matrix biologists can thus specialise in a particular class of molecule collagen proteoglycans elastin integrins fibrillins matrix metalloproteinases Specialities can also be by the particular ECM under study cartilage skin bone tumours Many matrix biologists also work closely with medical specialists and specialise in a particular disease or pathology rheumatology studying the change in ECM in cartilage and synovium in joints from rheumatoid or osteoarthritis patients orthopedics studying pathological and traumatically injured cartilage and tendon oncology studying how tumours and other cancers grow new ECM, metastasise and invade ECM of other tissues orthodontics studying how bone remodels around teeth dermatology studying ECM involved in wound healing and disease states such as scleroderma There are many matrix biology societies who hold meetings regularly all over the world. These meetings generate a forum for matrix biologists to discuss common interests and form collaborations ISMB International Society for Matrix Biology ref http www.ismb.org ref ASMB American Society for Matrix Biology ref http www.asmb.net ASMB American Society for Matrix Biology Home Page Bot generated title ref MBSANZ Matrix Biology Society of Australia and New Zealand ref http www.matrix.org.au Matrix Biology Bot generated title ref BSMB British Society for Matrix Biology ref http www.bsmb.ac.uk Home Bot generated title ref External links references DEFAULTSORT Matrix Biology Category Cell biology biology stub ja ... more details
In mathematics , a unitary matrix is a square math n times n math complex number complex matrix mathematics matrix math U math satisfying the condition math U dagger U UU dagger I n , math where math I n math is the identity matrix in n dimensions and math U dagger math is the conjugate transpose also called the Hermitian adjoint of math U math . Note this condition implies that a matrix math U math is unitary if and only if it has an inverse matrix inverse which is equal to its conjugate transpose math U dagger , math math U 1 U dagger , math A unitary matrix in which all entries are real is an orthogonal matrix . Just as an orthogonal matrix math G math preserves the real number real inner ... also a unitary matrix math U math satisfies math langle Ux, Uy rangle langle x, y rangle math for all ... product on math mathbb C n math . If math U , math is an math n times n math matrix then the following ... U , math is a normal matrix with eigenvalues lying on the unit circle . Properties All unitary matrices are normal matrix normal , and the spectral theorem therefore applies to them. Thus every unitary matrix math U math has a decomposition of the form math U V Sigma V dagger math where math V math is unitary, and math Sigma math is diagonal and unitary. That is, a unitary matrix is diagonalizable matrix diagonalizable by a unitary matrix. For any unitary matrix math U math , the following hold ... Mechanics edition 2nd page 39 isbn 0 306 40397 8 ref Eigenspaces are orthogonal if matrix is normal ... of all n by n unitary matrices with matrix multiplication forms a group mathematics group , called unitary group U n . Any unit norm matrix is the average of two unitary matrices. As a consequence, every math n times n math matrix is a linear combination of two unitary matrices. ref cite book first1 ... 1 ref See also Orthogonal matrix Hermitian matrix Symplectic matrix Unitary group Special unitary group Unitary operator Matrix decomposition Identity matrix References reflist External links MathWorld ... more details
In mathematics , especially in linear algebra and matrix theory , the commutation matrix is used for transforming the vectorized form of a matrix mathematics matrix into the vectorized form of its transpose . Specifically, the commutation matrix K sup m,n sup is the mn mn matrix which, for any m n matrix A , transforms vec A into vec A sup T sup K sup m,n sup vec A vec A sup T sup . Here vec A is the mn 1 column vector obtain by stacking the columns of A on top of one another vec A A sub 1,1 sub , ..., A sub m,1 sub , A sub 1,2 sub , ..., A sub m,2 sub , ..., A sub 1,n sub , ..., A sub m,n sub sup T sup where A A sub i,j sub . The main use of the commutation matrix, and the source of its name, is to commute the Kronecker product for every m n matrix A and every r q matrix B , K sup r,m sup A math otimes math B K sup n,q sup B math otimes math A . References Jan R. Magnus and Heinz Neudecker 1988 , Matrix Differential Calculus with Applications in Statistics and Econometrics , Wiley. Category Linear algebra Category Matrices Linear algebra stub sl Komutacijska matrika ... more details
For the club in San Francisco The Matrix club Matrix is a club in Berlin which opened in 1996. Located at Warschauer Platz 18 in ten basement vaults of the Berlin Warschauer Stra e station Warschauer Stra e railway station , the discoth que houses up to nine bars and five dance floors. The venue is with an overall size of 2.100 square meters one of the biggest clubs in Berlin. Between 1996 and 2002 many international known discjockeys like Marusha , Chris Isaac , Westbam , Underground Resistance , Josh Wink , Lords of the Underground , Lady B , Sven V th , Paul van Dyk and other exponents of electronic music performed in the Matrix. Since 2003 the programming is enlarged. Artists who have performed in recent years are Sabrina Setlur , Ne Yo , Georges Morel , Vibe Kingz , DJ Size and others. About three years the club had an own truck at the Berlin Love Parade . The venue is also used for showcases and filmsets. External links http www.matrix berlin.de Official Matrix Berlin website coord 52 30 16 N 13 26 56 E region DE BE type landmark source kolossus dewiki display title Category Nightclubs in Germany Matrix Club Category Music in Berlin Matrix Club da Matrix club de Matrix Club fr Matrix club no Matrix klubb sv Matrix nattklubb ... more details
In mathematics , a bisymmetric matrix is a square matrix mathematics matrix that is symmetric about both of its main diagonals. More precisely, an n n matrix A is bisymmetric if it satisfies both A A sup T sup and AJ JA where J is the n n exchange matrix . For example math begin bmatrix a & b & c & d & e b & f & g & h & d c & g & i & g & c d & h & g & f & b e & d & c & b & a end bmatrix . math Properties Bisymmetric matrices are both symmetric centrosymmetric matrix centrosymmetric and symmetric persymmetric matrix persymmetric . It has been shown that real valued bisymmetric matrices are precisely those symmetric matrices whose eigenvalues are the same up to sign after pre or post multiplication by the exchange matrix ref name simax0 cite journal last Tao first D. coauthors Yasuda, M. title A spectral characterization of generalized real symmetric centrosymmetric and generalized real symmetric skew centrosymmetric matrices journal SIAM J. Matrix Anal. Appl. volume 23 issue 3 pages 885 895 year 2002 url http siamdl.aip.org getabs servlet GetabsServlet?prog normal&id SJMAEL000023000003000885000001&idtype cvips&gifs Yes accessdate 2007 10 12 doi 10.1137 S0895479801386730 ref . The product of two bisymmetric matrices results in a centrosymetric matrix References reflist DEFAULTSORT Bisymmetric Matrix Category Matrices eu Matrize bisimetriko sl Bisimetri na matrika th ... more details
distinguish Polynomial matrix In mathematics, a matrix polynomial is a polynomial with matrix mathematics matrices as variables. Examples include math P A sum i 0 n a i A i a 0 I a 1 A a 2 A 2 cdots a n A n, math where P is a polynomial, math P x sum i 0 n a i x i a 0 a 1 x a 2 x 2 cdots a n x n, math and I is the identity matrix. math left A,B right A B B A, math the commutator Ring theory commutator of A and B . A matrix polynomial equation is an equality between two matrix polynomials, which holds for the specific matrices in question. If math P A Q A math , where A is a matrix over a field , then the eigenvalues of A satisfy the characteristic equation Disputed inline Characteristic equation date October 2010 math P lambda Q lambda math . br A matrix polynomial identity is a matrix polynomial equation which holds for all matricies A in a specified matrix ring M sub n sub R . DEFAULTSORT Matrix Polynomial Category Matrices Category Polynomials algebra stub ... more details
In linear algebra , a diagonal matrix is a matrix mathematics matrix usually a square matrix in which .... Thus, the matrix D d sub i,j sub with n columns and n rows is diagonal if math d i,j 0 mbox if i ne j qquad forall i,j in 1, 2, ldots, n . math For example, the following matrix is diagonal math begin bmatrix 1 & 0 & 0 0 & 4 & 0 0 & 0 & 3 end bmatrix math The term diagonal matrix may sometimes refer to a rectangular diagonal matrix , which is an m by n matrix with only the entries of the form ... square diagonal matrix is also a symmetric matrix . Also, if the entries come from the field mathematics field R or C , then it is a normal matrix as well. Equivalently, we can define a diagonal matrix as a matrix that is both triangular matrix upper and triangular matrix lower triangular . The identity matrix I sub n sub and any square zero matrix are diagonal. A one dimensional matrix is always diagonal. Scalar matrix Linked from Scalar matrix and Scalar transformation A diagonal matrix with all its main diagonal entries equal is a scalar matrix , that is, a scalar multiple &lambda I of the identity matrix I . Its effect on a vector is scalar multiplication by &lambda . For example, a 3× 3 scalar matrix has the form math begin bmatrix lambda & 0 & 0 0 & lambda & 0 0 & 0 & lambda end ... generally free module s math M cong R n math , for which the endomorphism algebra is isomorphic to a matrix ... they are denoted by Z V , follow the usual notation for the center. Matrix operations The operations of matrix addition and matrix multiplication are especially simple for diagonal matrices. Write diag a sub 1 sub ,..., a sub n sub for a diagonal matrix whose diagonal entries starting in the upper ... sub and for matrix multiplication , diag a sub 1 sub ,..., a sub n sub · diag b sub 1 sub ,..., b sub n sub diag a sub 1 sub b sub 1 sub ,..., a sub n sub b sub n sub . The diagonal matrix diag a sub 1 sub ,..., a sub n sub is invertible matrix invertible if and only if the entries a sub 1 sub ... more details
Unreferenced auto yes date December 2009 In numismatics , a matrix is an intermediate Molding process mould used in the process of manufacturing coin s. A matrix has its design in the same sense as a Die manufacturing die . The design is engraved convex into the matrix, which is used to create punch numismatics punches . The matrix step was developed in the 17th century for two main reasons. The original design in the matrix could be better preserved, as a single matrix could be used to make several punches. Second, it made easier the addition of secondary details such as the legend, otherwise a difficult task. In a similar sense, a matrix is the term for a Molding process mould or Die manufacturing die used for making a Sealing wax wax , metal or clay Seal emblem seal intended for purposes of authentication. DEFAULTSORT Matrix Numismatics Category Numismatics Category Seals insignia Coin stub it Matrice incisione ... more details
Orphan date February 2009 In mathematical modelling in epidemiology , the WAIFW matrix is an abbreviation for the Who Acquires Infection From Whom matrix. This describes the rate of transmission of infection between different groups in a population, such as people of different ages. Category Epidemiology infectious disease stub ... more details
Infobox company company name Matrix Partners company logo Image MatrixLogoFinal.JPG 175px Matrix Partners ... raised since inception ref homepage http www.matrixpartners.com www.matrixpartners.com Matrix ..., China . Matrix Partners is not connected with Matrix Private Equity Partners LLP or Matrix Securities, which are part of Matrix Group, a UK financial services business based in London ref http www.matrixgroup.co.uk Matrix Group website ref . History Tracing its roots to 1977, Matrix was an active ... . Among the firm s notable investments, Matrix Partners was an early stage investor in Apple ... , VERITAS Software , Vermeer Technologies Incorporated , and Xilinx . In 1985, Matrix raised its first institutional investor institutional private equity fund . Since then, Matrix has raised nine funds with total investor commitments of 2.4 billion. In 2001, Matrix Partners completed fundraising for Matrix Partners VII, a 1 billion venture capital fund. ref http www.altassets.com roundup arc 2001 nz103.php 1bn fund for Matrix Partners . AltAssets, 2001 ref In 2006, Matrix raised Matrix ... summary 0286 17548627 ITM Matrix makes plans for 445m fund. Matrix Partners raises funds for its new fund Matrix Partners VIII . Private Equity Week, 2006 ref In 2006, Matrix also raised a separate 150 million India fund. ref http www.altassets.com news arc 2006 nz9161.php Matrix Partners closes India fund on 150m . AltAssets, 2006. ref ref http dealbook.blogs.nytimes.com 2006 08 03 matrix closes new india fund Matrix Closes New India Fund . New York Times, 2006 ref In July 2009, Matrix Partners raised Matrix IX fund with 600m ref http www.matrixpartners.com site press detail 343 ref . References ... This Time . San Francisco Chronicle http www.thedeal.com techconfidential vc ratings matrix partners david skok pro.php Matrix Partners David Skok profits again this time from Tabblo . The Deal , 2007 http www.thefunded.com funds show Matrix Partners Matrix Partners Profile . The Funded http ... more details
Unreferenced date November 2006 In mathematics , an involutory matrix is a matrix mathematics matrix that is its own inverse. That is, matrix A is an involution if and only if A sup 2 sup I . One of the three classes of elementary matrix is involutory, namely the row interchange elementary matrix . A special case of another class of elementary matrix, that which represents multiplication of a row or column by &minus 1, is also involutory it is in fact a trivial example of a signature matrix , all of which are involutory. Involutory matrices are all square root of a matrix square roots of the identity matrix . This is simply a consequence of the fact that any nonsingular matrix multiplied by its inverse is the identity. If A is an n n matrix, then A is involutory if and only if A I is idempotent . An involutory matrix which is also symmetric matrix symmetric is an orthogonal matrix , and thus represents an isometry a linear transformation which preserves Euclidean distance . A Reflection linear algebra reflection matrix is an example of an involutory matrix. Clearly, any block diagonal matrix block diagonal matrices constructed from involutory matrices will also be involutory, as a consequence of the linear independence of the blocks. Examples Some simple examples of involutory matrices are shown below. math begin array cc mathbf I begin pmatrix 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 end pmatrix & mathbf I 1 begin pmatrix 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 ... I is the identity matrix which is trivially involutory R is a matrix with a pair of interchanged rows S is a signature matrix . An interesting general condition exists, for 2 × 2 matrices, where any matrix that may be written in the form A or A sup T sup below math mathbf A begin pmatrix ... pmatrix math is involutory. For example, for a matrix M of this form, where we set a 1, b 1, we ... Affine involution DEFAULTSORT Involutory Matrix Category Matrices es Matriz involutiva it Matrice involutoria ... more details
A complex number complex Matrix mathematics Square matrices and related definitions square matrix mathematics matrix A is a normal matrix if math A A AA math where A is the conjugate transpose of A . That is, a matrix is normal if it commutes with its conjugate transpose. If A is a real number real matrix, then A A sup T sup . Hence, the matrix is normal if A sup T sup A AA sup T sup . Normality is a convenient test for diagonalizable diagonalizability every normal matrix can be converted to a diagonal matrix by a unitary matrix unitary transform , and every matrix which can be made diagonal by a unitary matrix unitary transform is also normal, but finding the desired unitary transform transform requires much more work than simply testing to see whether the matrix is normal. The concept of normal ... elements in C algebra s. As in the matrix case, normality means commutativity is preserved, to the extent ... of C algebras, more amenable to analysis. Special cases Among complex matrices, all unitary matrix unitary , hermitian matrix Hermitian , and Skew Hermitian matrix skew Hermitian matrices are normal. Likewise, among real matrices, all Orthogonal matrix orthogonal , Symmetric matrix symmetric , and skew symmetric matrix skew symmetric matrices are normal. However, it is not the case that all normal matrices are either unitary or skew Hermitian. As an example, the matrix math A begin pmatrix 1 ... & 1 1 & 1 & 2 end pmatrix A A. math The matrix A is neither unitary, Hermitian, nor skew Hermitian ... normal. If they commute, however, then this is true. If A is both a triangular matrix and a normal matrix, then A is diagonal matrix diagonal . This can be seen by looking at the diagonal entries of A sup sup A and AA sup sup , where A is a normal, triangular matrix. Consequences The concept ... theorem applies a matrix A is normal if and only if it can be represented by a diagonal matrix and a unitary matrix U by the formula math mathbf A mathbf U mathbf Lambda mathbf U math where math mathbf ... 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
A logical matrix , binary matrix , relation matrix , Boolean matrix , or 0,1 matrix is a matrix mathematics matrix with entries from the Boolean domain B 0, 1 . Such a matrix can be used to represent a binary relation between a pair of finite set s. Matrix representation of a relation If R is a Binary ... can be represented by the Adjacency matrix adjacency matrix M whose row and column indices index ... numbers of the matrix, the sets X and Y are indexed with positive integers i ranges from 1 to the cardinality ... , 1, 4 , 2, 2 , 2, 4 , 3, 3 , 4, 4 . The corresponding representation as a Boolean matrix is math begin ... A permutation matrix is a 0,1 matrix, all of whose columns and rows each have exactly one nonzero element. A Costas array is a special case of a permutation matrix An incidence matrix in combinatorics ..., blocks of a block design , or edges of a graph mathematics A design matrix in analysis of variance is a 0,1 matrix with constant row sums. An adjacency matrix in graph theory is a matrix whose ... matrix of a simple graph simple , undirected graph is a binary symmetric matrix with zero diagonal. The biadjacency matrix of a simple, undirected bipartite graph is a 0,1 matrix, and any 0,1 matrix ... n smooth numbers can be described as a m × n 0,1 matrix, where is the prime counting ... pixel s in only two colors can be represented as a 0,1 matrix in which the 0 s represent pixels of one color and the 1 s represent pixels of the other color. Using binary matrix to check the game rules in the game of Go http senseis.xmp.net ?BinMatrix Some properties The matrix representation of the Equality mathematics equality relation on a finite set is an identity matrix , that is, one whose ... , where addition corresponds to logical OR and multiplication to logical AND , the matrix representation of the composition of relations composition of two relations is equal to the matrix product of the matrix representations of these relation. Frequently operations on binary matrices are defined ... more details
Advert date December 2007 O Matrix is a matrix programming language for mathematics , engineering , science , and financial analysis, marketed by Harmonic Software. The language is designed for High performance computing solutions. O Matrix is an integrated technical computing environment and matrix based scripting language. The O Matrix environment includes hundreds of mathematical, statistical, engineering and visualization functions. The diverse set of analysis functions enable the rapid development of complex, computationally intensive scientific, mathematical and engineering solutions. The O Matrix integrated environment provides a mode that is largely compatible with version 4 of the MATLAB language in the commercial product from MathWorks . More recent features of MATLAB , such as non numeric data types structures, cell arrays and objects , error handling with try catch, and nested and anonymous functions, are missing in O Matrix. The O Matrix environment includes a virtual machine of the O Matrix language to enable re distribution of solutions. External links http www.omatrix.com O Matrix site Harmonic Software . http www.scientificweb.com ncrunch ncrunch5.pdf Comparison of mathematical programs for data analysis ScientificWeb Category Array programming languages Category Numerical programming languages compu lang stub ... more details
In linear algebra , two rectangular m by n matrix mathematics matrices A and B are called equivalent if math B Q 1 A P math for some invertible matrix invertible n by n matrix P and some invertible m by m matrix Q . Equivalent matrices represent the same linear map linear transformation V W under two different choices of a pair of Basis linear algebra bases of V and W , with P and Q being the change of basis matrices in V and W respectively. The notion of equivalence should not be confused with that of Similar matrix similarity , which is only defined for square matrices, and is much more restrictive similar matrices are certainly equivalent, but equivalent square matrices need not be similar . That notion corresponds to matrices representing the same endomorphism V V under two different choices of a single basis of V , used both for initial vectors and their images. Properties Matrix equivalence is an equivalence relation on the space of rectangular matrices. For two rectangular matrices of the same size, their equivalence can also be characterized by the following conditions The matrices can be transformed into one another by a combination of elementary row operation elementary row and column operations . The matrices have the same rank of a matrix rank . See also Similar matrix Row equivalence Matrix congruence Category Matrices de quivalenz Matrix nl Equivalente matrices sl Ekvivalentna matrika fi Matriisiekvivalenssi zh ... more details
orphan date December 2009 Infobox award name The Matrix Awards image description Excellence in Mass media media achievements presenter country United States year 1970 website http www.nywici.org matrixorg The Matrix Awards is an annual awards ceremony started in 1970 to honor exceptional women in the media in the fields of arts, advertising, entertainment, film, television, theater, books, broadcasting, magazines, newspapers, public relations and new media. Each winner is given a Matrix Award, joining past winners such Alice Walker , Eve Ensler , Katie Couric , Avery Corman Judy Corman Judy Corman , Anna Deavere Smith , Meryl Streep , Nora Ephron , Arianna Huffington , Toni Morrison , Barbara Walters , Rosie O Donnell , Anna Quindlen , Meredith Vieira , Michelle Pfeiffer , Ellen DeGeneres , Christiane Amanpour , Amy Tan , Gloria Steinem and Edie Falco . Sources http www.nationalreview.com blyth blyth200504140804.asp http www.mediabistro.com fishbowlny parties the matrix awards media revolutionaries 34762.asp http www.huffingtonpost.com ariane de bonvoisin the matrix awards b 95602.html http www.portfolio.com views blogs mixed media 2008 04 07 on the scene at the matrix awards http www.nywici.org matrix http www.awcdc.net matrixawards 09.shtml http www.bizbash.com newyork content editorial 7626 aol hosts packed matrix awards.php http www.zimbio.com pictures lsAys0Xpuks 2009 Matrix Awards 3Qmd39vor2g Meredith Vieira DEFAULTSORT Matrix Award Category Awards and prizes honoring women Category Media awards Category Awards established in 1970 ... more details
File Walsh 16 Gould s Morse.svg thumb 320px Walsh matrix of order 16 multiplied with a vector File Natural and sequency ordered Walsh 16.svg thumb 320px Natural ordered Hadamard matrix permuted into sequency ordered Hadamard matrix br br The number of sign changes per row in the natural ordered matrix is br 0,15, 7,8, 3,12, 4,11, 1,14, 6,9, 2,13, 5,10 , br in the sequency ordered matrix the number of sign changes is consecutive. File LDU decomposition of Walsh 16.svg thumb 320px LU decomposition LDU decomposition of a Walsh matrix br The ones in the triangular matrices form Sierpinski triangle Sierpinski triangles . The entries of the diagonal matrix are values from oeis A001316 Gould s sequence , with the minus signs distributed like the ones in Thue Morse sequence . File Binary Walsh matrix 16.svg thumb 320px Binary Walsh matrix as a w Matrix multiplication matrix product br The binary matrix white 0, red 1 is the result ... in Real number R . In mathematics , a Walsh matrix is a specific Matrix mathematics Square matrices and related definitions square matrix , with dimensions a power of 2, the entries of which are 1 .... The Walsh matrix was proposed by Joseph Leonard Walsh in 1923. ref name kanjilal Each row of a Walsh matrix corresponds to a Walsh function . The natural ordered Hadamard matrices Hadamard matrix is defined by the Recursion recursive formula below, and the sequency ordered Hadamard matrix is formed ... to either matrix as the Walsh matrix. The Walsh matrix and Walsh function s are used in computing ... by the recursive formula The lowest order of Hadamard matrix is 2 math H 2 1 begin bmatrix ... matrix can be derived from the ordering of the Hadamard matrix by first applying the bit reversal ... Category Walsh matrix Walsh matrix Haar wavelet Quincunx matrix Hadamard transform Code division multiple access Notes reflist DEFAULTSORT Walsh Matrix Category Matrices it Matrice di Walsh sl Walshova ... more details
Refimprove date August 2009 Infobox character colour black colour text red name Merovingian series The Matrix franchise The Matrix image File Merovingian200px.png 200px caption Lambert Wilson as the Merovingian in The Matrix Reloaded first last cause creator The Wachowskis Wachowski brothers portrayer Lambert Wilson The Matrix Reloaded and The Matrix Revolutions br Robin Atkin Downes The Matrix Path of Neo episode nickname alias The Frenchman species Computer program gender Male age born death specialty occupation title callsign family spouse Persephone The Matrix Persephone significantother children relatives residence religion nationality The Merovingian also known as the Frenchman , and called Merv by Trinity is a fictional character and the supporting antagonist of the films The Matrix Reloaded and The Matrix Revolutions . He is portrayed by Lambert Wilson in both films and voiced by Robin Atkin Downes in The Matrix Path of Neo . He also played a prominent role in The Matrix Online role playing game. The Merovingian provides a safe haven for exiled or obsolete programs in the Matrix, as an alternative to deletion. Being an exile himself, the Merovingian s services are not condoned ... both he and the Oracle The Matrix Oracle say, he was a program made to regulate behavior amongst the Bluepills and report back with results. After the collapse of the first Matrix, he became obsolete ref name TMR The Matrix Reloaded ref as the newer versions presented an illusion of choice to the hard ... straightforward methods. Instead of accepting deletion, he retreated into the programming of the Matrix ... royalty. His wife Persephone The Matrix Persephone is named after Persephone , the Greek gods and goddesses ... links IMDB character 0000758 Merovingian Matrix Category Matrix characters Merovingian Category ... Category Fictional characters introduced in 2003 film char stub es Merovingio Matrix it Il Merovingio pl Merowing Matrix pt Merovingian Matrix ru uk ... more details
DISPLAYTITLE Oracle The Matrix Infobox character colour green colour text lightgreen name The Oracle series The Matrix franchise The Matrix image Image The Oracle i .gif caption Gloria Foster as the Oracle. first The Matrix last The Matrix Revolutions cause creator The Wachowskis Wachowski Brothers portrayer Gloria Foster The Matrix and The Matrix Reloaded br Mary Alice The Matrix Revolutions episode ... nationality The Oracle is a fictional character in The Matrix franchise The Matrix franchise . She ... films and Mary Alice in the third film. The character also appears in the video game Enter the Matrix and the MMORPG The Matrix Online . Overview In the first film, she is a mysterious but powerful figure ... Matrix fictional universe the Matrix s system. Later, she is revealed to be a Sapience sapient computer program program who is integral to the very nature of the Matrix itself. Whether her power ... power cannot be used to predict the ultimate consequences of Neo The Matrix Neo , who possesses free will when he defies the Architect The Matrix Architect . Her power of foresight, on the other ... thus, allowing the Matrix to become more accustomed for the majority of the human population to accept. She exhibits a trait for predicting events directly relevant to the nature and or programming of the Matrix ... is her prediction about Neo s choice in the second movie, The Matrix Reloaded she had existed ... .jpg thumb left Mary Alice as the Oracle. The Oracle is played by Gloria Foster in The Matrix and The Matrix Reloaded , and by Mary Alice in The Matrix Revolutions and Enter the Matrix , one of the franchise s video games. In The Matrix Revolutions and Enter the Matrix , it is explained that Kamala ... code in exchange for their daughter s passage into the Matrix as an Exile via the Trainman. In reality ... role in Matrix Revolutions was shot. In the third Matrix movie, the Oracle hints at her true purpose, which is to bring imbalance, rather than balance, to the equations that form the Matrix. In that she ... more details
Merge to Z matrix mathematics date July 2010 In mathematics , especially linear algebra , an M matrix is a Z matrix mathematics Z matrix with eigenvalue s whose real number real parts are positive. M matrices are a subset of the class of P matrix P matrices , and also of the class of inverse positive matrices i.e. matrices with inverses belonging to the class of Nonnegative matrix positive matrices . ref Citation first Takao last Fujimoto lastauthoramp yes first2 Ravindra last2 Ranade title Two Characterizations of Inverse Positive Matrices The Hawkins Simon Condition and the Le Chatelier Braun Principle journal Electronic Journal of Linear Algebra volume 11 issue pages 59 65 year 2004 url http www.emis.ams.org journals ELA ela articles articles vol11 pp59 65.pdf . ref A common characterization of an M matrix is a non singular square matrix with non positive off diagonal entries and all principal minors positive, but many equivalences are known. The name M matrix was seemingly originally chosen by Alexander Ostrowski in reference to Hermann Minkowski . ref Citation first Abraham last Bermon lastauthoramp yes first2 Robert J. last2 Plemmons title Nonnegative Matrices in the Mathematical Sciences location Philadelphia publisher Society for Industrial and Applied Mathematics year 1994 page 134,161 Thm. 2.3 and Note 6.1 of chapter 6 isbn 0898713218 . ref A symmetric M matrix is sometimes called a Stieltjes matrix . M matrices arise naturally in some discretizations of differential operators, particularly those with a minimum maximum principle, such as the Laplacian, and as such are well studied in scientific computing. The LU decomposition LU factors of an M matrix are guaranteed to exist and can be stably computed without need for numerical pivoting, also have positive diagonal entries and non positive off diagonal entries. Furthermore, this holds even for incomplete LU factorization ... for iterative solution. See Also Metzler matrix Hurwitz matrix References references Category ... more details
In linear algebra , the identity matrix or unit matrix of size n is the n n square matrix with ones on the main diagonal and zeros elsewhere. It is denoted by I sub n sub , or simply by I if the size is immaterial or can be trivially determined by the context. In some fields, such as quantum mechanics , the identity matrix is denoted by a boldface one, 1 otherwise it is identical to I . math I 1 begin bmatrix 1 end bmatrix , I 2 begin bmatrix 1 & 0 0 & 1 end bmatrix , I 3 begin bmatrix 1 & 0 & 0 ... the Identity Matrix meaning Unit Matrix and Elementary Matrix , or from the German Einheitsmatrix , ref Identity Matrix On Wolfram s MathWorld http mathworld.wolfram.com IdentityMatrix.html ref respectively , although I is considered more universal. When A is m n , it is a property of matrix multiplication that math I mA AI n A. , math In particular, the identity matrix serves as the unit ... group GL n consisting of all invertible matrix invertible n n matrices. The identity matrix itself ... of the Basis linear algebra basis . The i th column of an identity matrix is the unit vector e sub i sub . It follows that the determinant of the identity matrix is 1 and the trace linear algebra trace is n . Using the notation that is sometimes used to concisely describe diagonal matrix ... using the Kronecker delta notation math I n ij delta ij . , math The identity matrix also has the property ... of one another. The identity matrix of a given size is the only idempotent matrix of that size having full rank . That is, it is the only matrix such that a when multiplied by itself the result is itself ... . The Square root of a matrix principal square root of an identity matrix is itself, and this is its only Positive definite matrix positive definite square root. However, every identity matrix with at least ... 2003, 499 500. ref See also Logical matrix Binary matrix Zero matrix Unitary matrix Notes references External links planetmath reference title Identity matrix id 1223 Category Abstract algebra Category ... more details
unreferenced date October 2007 In mathematics , a matrix unit is an idealisation of the concept of a Matrix mathematics matrix , with a focus on the algebraic properties of matrix multiplication . The topic is comparatively obscure within linear algebra , because it entirely ignores the numeric properties of matrices it is mostly encountered in the context of abstract algebra , especially the theory of semigroup s. Despite the name, matrix units are not the same as Identity matrix unit matrices or Unitary matrix unitary matrices . Two matrices can be multiplied when the number of columns in one is the same as the number of rows in the other otherwise, they are incompatible. The idea behind matrix units is to look at this fact in isolation a matrix unit is a matrix with dimensions, but with the entries scooped out. Let I be a nonempty Set mathematics set , to be used for counting the matrix rows and columns. There is no requirement for it to be finite indeed, standard matrix algebra would use the set of natural number s not including zero N sup sup . A matrix unit is either an ordered pair r , c , with r and c elements of I , or it is a special zero object, written as 0 . Multiplication is defined as follows 0 x x 0 0 for any matrix unit x r , c s , d r , d if c s , and 0 if c &ne s . The 0 element can be seen as an error symbol for when multiplication fails the first rule implies that errors propagate through an entire product containing a single incompatible combination. For example, the product with I N sup sup 2, 3 3, 2 2, 1 1, 4 2, 4 represents the abstract matrix multiplication ... of a matrix. Different letters are used in the A position to refer to matrix units on a different ... s and Rees matrix semigroup s. It also arises as the Trace semigroup theory trace of the unique Green ... of that class interacts with the structure of the semigroup s principal ideal s. A semigroup of matrix ... matrix units a , a for a in I , together with 0. Category Matrix theory Category Semigroup theory ... more details
In mathematics , a bidiagonal matrix is a matrix mathematics matrix with non zero entries along the main diagonal and either the diagonal above or the diagonal below. This means there are exactly two non zero diagonals in the matrix. When the diagonal above the main diagonal has the non zero entries the matrix is upper bidiagonal . When the diagonal below the main diagonal has the non zero entries the matrix is lower bidiagonal . For example, the following matrix is upper bidiagonal math begin pmatrix 1 & 4 & 0 & 0 0 & 4 & 1 & 0 0 & 0 & 3 & 4 0 & 0 & 0 & 3 end pmatrix math and the following matrix is lower bidiagonal math begin pmatrix 1 & 0 & 0 & 0 2 & 4 & 0 & 0 0 & 3 & 3 & 0 0 & 0 & 4 & 3 end pmatrix . math Usage One variant of the QR algorithm starts with reducing a general matrix into a bidiagonal one. ref Bochkanov Sergey Anatolyevich. ALGLIB User Guide General Matrix operations Singular value decomposition . ALGLIB Project. 2010 12 11. URL http www.alglib.net matrixops general svd.php. Accessed 2010 12 11. Archived by WebCite at http www.webcitation.org 5utO4iSnR ref and the Singular value decomposition uses this method as well. See also Diagonal matrix List of matrices LAPACK Bidiagonalization Hessenberg form The Hessenberg form is similar, but has more non zero diagonal lines than 2. Tridiagonal matrix with three diagonals References Stewart, G. W. 2001 Matrix Algorithms, Volume II Eigensystems . Society for Industrial and Applied Mathematics. ISBN 0 89871 503 2. Reflist External links http www.cs.utexas.edu users flame pubs flawn53.pdf High performance algorithms for reduction to condensed Hessenberg, tridiagonal, bidiagonal form Category Linear algebra Category Sparse matrices Linear algebra stub compu prog stub de Bidiagonalmatrix es Matriz bidiagonal eu Matrize bidiagonal sl Bidiagonalna matrika sv Bidiagonal matris ... more details
citations missing date May 2010 In mathematics , particularly matrix theory , a band matrix is a sparse matrix whose non zero entries are confined to a diagonal band , comprising the main diagonal and zero or more diagonals on either side. Matrix bandwidth Bandwidth sparse matrix , matrix bandwidth , bandwidth matrix , bandwidth matrix theory redirect here Formally, consider an n × n matrix A a sub i,j sub . If all matrix elements are zero outside a diagonally bordered band whose range is determined ... of the matrix is k sub 1 sub k sub 2 sub 1 in other words, it is the smallest number of adjacent diagonals to which the non zero elements are confined . A matrix is called a band matrix or banded matrix if its bandwidth is reasonably small. A band matrix with k sub 1 sub k sub 2 sub 0 is a diagonal matrix a band matrix with k sub 1 sub k sub 2 sub 1 is a tridiagonal matrix when k sub 1 sub k sub 2 sub 2 one has a pentadiagonal matrix and so on. If one puts k sub 1 sub 0, k sub 2 sub n &minus 1, one obtains the definition of an upper triangular matrix similarly, for k sub 1 sub n &minus 1, k sub 2 sub 0 one obtains a lower triangular matrix. Applications In numerical ... a matrix with a half bandwidth equal to the square root of the matrix dimension, but inside the band ... decomposition to such a matrix results in the band being filled in by many non zero elements. Band storage ... zero. For example, a tridiagonal matrix has bandwidth 1. The 6 by 6 matrix math begin bmatrix B 11 & B ... & cdots & 0 & B 65 & B 66 end bmatrix math is stored as the 6 by 3 matrix math begin bmatrix 0 & B ... & 0 end bmatrix . math A further saving is possible when the matrix is symmetric. For example, consider a symmetric 6 by 6 matrix with a right bandwidth of 2 math begin bmatrix A 11 & A 12 & A 13 & 0 ... & sym & & & A 55 & A 56 & & & & & A 66 end bmatrix . math This matrix is stored as the 6 by 3 matrix ... matrices. A band matrix can be likened in complexity to a rectangular matrix whose row dimension ... more details
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