A representationterm is a word, or a combination of words, that semantically represent the data type value domain of a data element. A representationterm is commonly referred to as a class word by those familiar with data dictionary data dictionaries . ISO IEC 11179 5 2005 defines representationterm as a designation of an instance of a representation class As used in ISO IEC 11179 , the representationterm is that part of a data element name that provides a semantic pointer to the underlying data type. A Representation class is a class of representations. This representation class provides a way to Taxonomic classification classify or group data element s. A RepresentationTerm may be thought ... Element Framework uses a subset of CCTS representation terms and assigns numeric codes to those used. Use cases for representationterm Managing Value Domains A value domain expresses the set of allowed values for a data element. The representationterm and typically the corresponding data type term .... Thus the representationterm can be used to control proliferation of value domains by ensuring equivalent value domains use the same representationterm. Finding equivalent properties When a person ... terms i.e. Sex or Gender is much more efficient in this respect. Inference The RepresentationTerm ... models for a wide variety of uses. In ISO 15000 5, the representationterm provides a mechanism to harmonize ... such as the Universal Data Element Framework which refer to a RepresentationTerm as a Property Word assign unique integer IDs to each RepresentationTerm. This allows metadata mapping tools to map ... consensus border 1 Sample Representation Terms Term Usage Amount Monetary value with units of currency ... a representationterm and the value domain it represents. This is caused by further qualifying the corresponding data type term. Standards that use Representation Terms ebXML Electronic Business ... to the type of data stored in the data element. ref reptermasattr Representation terms are typically ... more details
Wiktionarypar representation represent Representation can refer to Representation politics , one s ability to influence the political process Representative democracy Permanent Representation, a type of diplomatic mission Representation of the International NGO the representative office of the International non governmental organization INGO mission Representation arts , the depiction and ethical concerns of construction in visual arts and literature. Depiction is meaning conveyed through pictures Representation psychology , a hypothetical internal cognitive symbol that represents external reality Representation mathematics and group representation Multiple representations mathematics education Representation chemistry Representation systemics Knowledge representation , the study of formal ways to describe knowledge Legal representation or advocacy is provided by lawyers Lobbying for a group of individuals or companies In unionised workplaces, Union steward shop stewards and union executives can represent employees The legal status of a statement made with regards to Contract contract law A fiction of the law which causes a person to enter into another s right of succession, called Representation succession representation , and also called substitution . Represent can refer to Represent Fat Joe album Represent Fat Joe album , a 1993 album by Fat Joe Represent Compton s Most Wanted album Represent Compton s Most Wanted album , a 2000 album by Compton s Most Wanted Represent , a 1994 album by DJ Magic Mike Represent song Represent song , a song by Nas Represent , a 2009 song by The Red Jumpsuit Apparatus Represent Weezer song Represent , a 2010 single by Weezer released as an unofficial anthem for the United States men s national soccer team See also Reprazent disambig cs Reprezentace de Repr sentation es Representaci n fr Repr sentation homonymie nl Representatie pt Representa o ro Reprezentare ru simple Representation fi Representaatio sv Representation ... more details
wiktionary term short term medium term long termTerm may refer to Term language or terminology , a noun or compound word used in a specific context meaning Term computers or terminal emulator, a program that emulates a video terminal Term architecture or terminal form, a human head and bust that continues as a square tapering pillar like form Technical term , part of the specialized vocabulary of a particular field Contractual term , a legally binding provision Lengths of Term time time Academic term , a division of the academic year in which classes are held Easter term Lent term Michaelmas termTerm of office , the length of time a person serves in a particular office Term of patent , the maximum period during which a patent can be maintained in force In mathematics Term mathematics , a component of a mathematical expression Term logic , a component of a logical expression Ground term , a term with no variables Term algebra , the algebra of mathematical terms Term symbol , a concept in quantum mechanics See also Full term , at the end of the duration of a pregnancy Maxterms Minterms Term logic Tern disambiguation Terme disambiguation Termeh , a type of textile United States midterm election disambig ar be cv de Begriff eo Termino terminologio ka pl Termin ro Termen ru sr tr Terim uk yi ... more details
The term complex representation has slightly different meanings in mathematics and physics. In mathematics , a complex representation is a group representation of a group or Lie algebra on a complex vector space. In physics , a complex representation is a group representation of a group or Lie algebra on a complex vector space that is neither real representation real nor pseudoreal representation pseudoreal . In other words, the Group mathematics group elements are expressed as complex matrices, and the complex conjugate of a complex representation is a different, non equivalent representation. For compact groups, the Frobenius Schur indicator can be used to tell whether a representation is real, complex, or pseudo real. For example, the N dimensional fundamental representation of SU N for N greater than two is a complex representation whose complex conjugate is often called the antifundamental representation . algebra stub Category Representation theory of groups ... more details
A representationterm is a word, or a combination of words, used as part of a data element name . Representation class is sometimes used as a synonym for representationterm. In ISO IEC 11179 , a representation class provides a way to Taxonomic classification classify or group data element s. A representation class is effectively a specialized classification scheme . Hence, there is currently some discussion in ISO over the merits of keeping representation class as a separate entity in 11179, versus collapsing it into the general classification scheme facility ref Issue114 . A clear distinction between the two mechanisms, however, is that 11179 allows a data element to be classified by only one representation class, whereas there is no such restriction on other classification schemes. ISO IEC 11179 does not specify that representation terms should be drawn from the values of representation ... of consistency whatever that might mean between the representation terms used to name a data element, and the representation class used to classify it. The termrepresentation class has been used in metadata ... beyond how a data element is represented in a computer system . In practice this term is used to shed light on the semantics or meaning of the data element. Definitions of representation class There are several alternate definitions for representation class . Some of these are taken from the ISO documents ... rules. ISO Definitions of representation class From ISO IEC TR 20943 1 First edition 2003 08 01 pdf page 91 B.2.3 Representation class Representation class is the value domain for representation. The set ... element categorized with the representation class amount is different from an element categorized as number ... using them together. Representation class is a mechanism by which the functional and or presentational ... 02 15 3.3.51 data element representation class the class of representation of a data element See also ... to the ISO bugzilla discussion of Representation class External links http standards.iso.org ittf PubliclyAvailableStandards ... more details
Unreferenced stub auto yes date December 2009 Orphan date November 2006 Substantive representation in contrast to descriptive representation is a concept in the legislative branch es of Representation politics representative republic s describing the tendency of representatives to advocate for certain groups. Often, their area of advocacy is in contrast to their background, such as late United States U.S. United States Senate Senator Ted Kennedy Edward Kennedy s advocacy for the poor Kennedy was a scion of one of the richest families in Massachusetts . Constituents vote for representatives by looking at policy stances and past efforts as a representative. DEFAULTSORT Substantive Representation Category Political terms Poli term stub ... more details
In representation theory of Lie group s and Lie algebra s, a fundamental representation is an irreducible finite dimensional representation of a semisimple Lie algebra semisimple Lie group or Lie algebra whose highest weight is a fundamental weight . For example, the defining module of a classical Lie group is a fundamental representation. Any finite dimensional irreducible representation of a semisimple Lie group or Lie algebra can be constructed from the fundamental representations by a procedure due to lie Cartan . Thus in a certain sense, the fundamental representations are the elementary building blocks for arbitrary finite dimensional representations. Examples In the case of the general linear group , all fundamental representations are exterior power s of the defining module. In the case of the special unitary group SU n SU n , the n &minus 1 fundamental representations are the wedge products math operatorname Alt k mathbb C n math consisting of the alternating tensor s, for k 1, 2, ..., n &minus 1. The spin representation of the twofold cover of an odd orthogonal group , the odd spin group , and the two half spin representations ... that cannot be realized in the space of tensors. The adjoint representation of the simple Lie group of type E8 mathematics E sub 8 sub is a fundamental representation. Explanation The Representation ... group are indexed by their highest weight representation theory weights . These weights are the lattice ... and extract one copy of the irreducible representation corresponding to that dominant weight. Other uses Outside of Lie theory, the term fundamental representation is sometimes loosely used to refer to a smallest dimensional faithful representation, though this is also often called the standard or defining representation a term referring more to the history, rather than having a well defined mathematical meaning . References Fulton Harris Category Lie groups Category Representation theory algebra ... more details
In mathematics and theoretical physics , a bifundamental representation is a representation theory representation obtained as a tensor product of two fundamental representation fundamental or antifundamental representation antifundamental representations. For example, the MN dimensional representation M , N of the group math SU M times SU N math is a bifundamental representation. These representations occur in quiver diagram s. algebra stub Category Abstract algebra ... more details
In mathematics , an antifundamental representation is the complex conjugate of the fundamental representation , although the distinction between the fundamental and the antifundamental representation is a matter of convention. However, these two are often non equivalent, because each of them is a complex representation . Category Representation theory of Lie groups geometry stub ... more details
that system. The termrepresentation of a group is also used in a more general sense to mean any description of a group as a group of transformations of some mathematical object. More formally, a representation ...In the mathematics mathematical field of representation theory , group representations describe abstract ... is a vector space we have a linear representation . Some people use realization for the general notion and reserve the termrepresentation for the special case of linear representations. The bulk of this article describes linear representation theory see the last section for generalizations. Branches of group representation theory The representation theory of groups divides into subtheories ... divides the order of the group, then this is called modular representation theory this special case has very different properties. See Representation theory of finite groups . Compact group s or locally compact group s &mdash Many of the results of finite group representation theory are proved by averaging ..., so the results of compact representation theory apply to them. Other techniques specific ..., and their representation theory is crucial to the application of group theory in those fields. See ... groups is too broad to construct any general representation theory, but specific special cases .... Representation theory also depends heavily on the type of vector space on which the group acts ... A representation of a group mathematics group G on a vector space V over a field mathematics ... of a vector space general linear group on V . That is, a representation is a map math rho colon G to GL ... Here V is called the representation space and the dimension of V is called the dimension of the representation. It is common practice to refer to V itself as the representation when the homomorphism is clear ... , a continuous representation of G on V is a representation such that the application math Phi G times ... of a representation of a group G is defined as the normal subgroup of G whose image under ... more details
The adjoint representation can refer to Ad the adjoint representation of a Lie group G ad the adjoint representation of a Lie algebra math mathfrak g math , see adjoint endomorphism . mathdab ... more details
In mathematics , a linear representation &rho of a group G is a monomial representation if there is a finite index subgroup H and a one dimensional linear representation &sigma of H , such that &rho is equivalent to the induced representation Ind sub H sub sup G sup &sigma . Alternatively, one may define it as a representation whose image is in the monomial matrices . Here for example G and H may be finite group s, so that induced representation has a classical sense. The monomial representation is only a little more complicated than the permutation representation of G on the coset s of H . It is necessary only to keep track of scalars coming from &sigma applied to elements of H . References Springer id Monomial representation title Monomial representation Category Representation theory of groups Algebra stub it Rappresentazione monomiale ... more details
Democracy In politics , representation describes how some individuals stand in for others or a group of others, for a certain time period. Representation usually refers to representative democracy representative ... in the legislature . Generally, only citizen s are granted representation in the government in the form ... Fenichel Pitkin established four theories of representation ref http plato.stanford.edu entries political representation PitFouVieRep Political Representation Stanford Encyclopedia of Philosophy ref Formalistic Representation, including Authorization Accountability Symbolic Representation Descriptive Representation, and Substantive Representation Burke British politician Edmund Burke in his 1774 ... of representation against the notion that elected officials should be delegates who exactly ... Pitkin, The concept of representation 1972 p. 174 ref Representation by population This section ... where travel is difficult and distances are long. The shortened term rep by pop is used in Britain ... districts in order to give meaningful representation to remote communities, and only in urban and suburban ... the US, the UK and Canada respectively . Representation by area This section is linked from United States ... Senators per state, at least one United States House of Representatives Representative per state, and representation ... unequal representation in Parliament in the Commons as well as the Senate relative to Ontario, British ... areas and overwhelmingly urban areas is one reason why the realities of representation by area still have sway against the ideal of representation by population. Descriptive representation Ref improve section date July 2008 Descriptive representation is the idea that elected representatives in democracies ... black legislators. Sometimes voting systems that obtain proportional representation may achieve descriptive representation as well. However this can be guaranteed only to the extent that voting ... representation increases, distrust decreases. This can be the basis of laws imposing that half ... more details
In number theory , cuspidal representations are certain group representation representations of algebraic groups that occur discretely in math L 2 math spaces. The term cuspidal is derived, at a certain distance, from the cusp form s of classical modular form theory. In the contemporary formulation of automorphic representation s, representations take the place of holomorphic functions these representations may be of adelic algebraic group s. When the group is the general linear group math operatorname GL 2 math , the cuspidal representations are directly related to cusp forms and Maass form s. For the case of cusp forms, each Hecke eigenform newform corresponds to a cuspidal representation. Formulation Let G be a reductive group reductive algebraic group over a number field K and let A denote the adele group adele s of K . Let Z denote the center of a group centre of G and let be a continuous mathematics continuous character mathematics unitary character from Z K Z A sup × sup to C sup × sup . Fix a Haar measure on G A and let L sup 2 sup sub 0 sub G K G A , denote the Hilbert space of measurable function measurable complex valued functions, f , on G A satisfying f g f g for all G K f gz f g z for all z Z A math int Z mathbf A G K backslash G mathbf A f g 2 ,dg infty math math int U K backslash U mathbf A f ug ,du 0 math for all unipotent radical s, U , of all proper parabolic subgroup s of G A . This is called the space of cusp forms with central character on G A . A function occurring in such a space is called a cuspidal function . This space is a unitary representation of the group G A where the group action action of g G A on a cuspidal function ... pi m pi V pi math where the sum is over irreducible representation irreducible subrepresentation s of L ... occurs with finite multiplicity . A cuspidal representation of G A is such a subrepresentation ... Murty. Lectures on Automorphic L functions 2004 , Chapter 5. Category Representation theory of algebraic ... more details
group Grrl Activistas who catalogue what they term as the mis representation of rape in British broadcast ... to differentiate between actual rape and its knowledge representationrepresentation and to ask questions ... arges that the term rape culture says more about the prominent status of rape as a central trope within ... of the visual representation of rape. One of the myths which is perpetuated by these representations ... the relationship between the visual representation of rape and post feminism , examining depictions ... communication technologies allow rape survivors to counteract this so called mis representation ... reflist cite book title Rape and Representation author Higgins, Lynn A, and Silver, Brenda R ... more details
the more general notion of representations throughout mathematics representation mathematics Representation ... on representation theory include Harvtxt Curtis Reiner 1962 and Harvtxt Serre 1977 . Other excellent sources are Harvtxt Fulton Harris 1991 and Harvtxt Goodman Wallach 1998 . ref In essence, a representation ... representationrepresentation theory of groups , in which elements of a group are represented by invertible ... of the representation theory of finite groups, see Harvtxt Lam 1998 . For algebraic and Lie groups, see Harvtxt Borel 2001 . ref Representation theory is a powerful tool because it reduces problems ... . ref Representation theory is also important in physics because, for example, it describes how ... name Sternberg Harvnb Sternberg 1994 . ref A striking feature of representation theory is its pervasiveness in mathematics. There are two sides to this. First, the applications of representation theory are diverse ref Harvnb Lam 1998 p 372 . ref in addition to its impact on algebra, representation ... 1979 , Harvnb Gelbert 1984 . ref The second aspect is the diversity of approaches to representation ... footnotes and also Harvtxt Borel 2001 . ref The success of representation theory has led to numerous ... Simson Skowronski Assem 2007 . ref The algebraic objects to which representation theory applies ... real or complex number s respectively. In this case, the idea of representation theory is to do abstract ... is a group under matrix multiplication and the group representationrepresentation theory of groups ... and hence there is a corresponding representation of an associative algebra representation theory of associative ... , then the n × n matrices become instead a Lie algebra, leading to a representation of a Lie algebra representation theory of Lie algebras . This generalizes to any field F and any vector space ... group representation algebra representation Lie algebra representation There are two ways to say what a representation is. ref This material can be found in standard textbooks, such as Harvtxt Curtis ... more details
Symbolic representation may refer to Symbolism disambiguation Symbolic linguistic representation In politics, it has to do with a representative in congress or in a group that is seen as being there to represent a group of minorities whether it be gender or cultural groups. See also Symbolic disambiguation Representation disambiguation disambig ... more details
. 13 The termrepresentation carries a range of meanings and interpretations. In literary theory , representation ... is the representation of the word or sound. For example, when referring to the term sister signifier ...Representation is the use of signs that stand in for and take the place of something else. ref name Mitchell1995 Mitchell, W. 1995, Representation , in F Lentricchia & T McLaughlin eds , Critical Terms for Literary Study , 2nd edn, University of Chicago Press, Chicago ref It is through representation ... Representation has been associated with aesthetics art and semiotics signs . Mitchell says representation ..., Media and society an introduction , 3rd edn, Oxford University Press, South Melbourne, 2005 ref Representation .... ref name Stadler2005 Defining representation Image Mona Lisa, by Leonardo da Vinci, from C2RMF retouched.jpg ... re , intensive prefix, praesentare to present, lit. to place before . A representation is a type of recording ... in a Media arts medium . The degree to which an artistic representation resembles the object it represents ... in Hadrian s Villa mosaic Since ancient times representation has played a central role in understanding ... theory who considered literature as simply one form of representation. ref name Childers1995 Childers ..., New York, 1995 ref Aristotle for instance, considered each mode of representation, verbal, visual or musical, as being natural to human beings. ref name Vukcevich2002 Vukcevich, M 2002, Representation ... animals is their ability to create and manipulate signs. ref name Mitchell1990 Mitchell, W, Representation ..., in contrast, looked upon representation with more caution. He recognised that literature is a representation ... Practice , Open University Press, London, 1997. ref For Plato, representation, like contemporary ... things . Plato believed that representation needs therefore, to be controlled and monitored due to the possible ... name Mitchell1995 From childhood man has an instinct for representation, and in this respect man differs ... things. ref name Mitchell1995 p. 11 Aristotle discusses representation in three ways The object ... more details
In mathematics , if G is a group mathematics group and &rho is a linear representation of it on the vector space V , then the dual representation Overline &rho is defined over the dual vector space Overline V as follows ref Lecture 1 of Fulton Harris ref Overline &rho g is the transpose of a linear map transpose of &rho g sup &minus 1 sup for all g in G . Then Overline &rho is also a representation, as may be checked explicitly. The dual representation is also known as the contragredient representation . If math mathfrak g math is a Lie algebra and &rho is a representation of it over the vector space V , then the dual representation Overline &rho is defined over the dual vector space Overline V as follows ref Lecture 8 of Fulton Harris ref Overline &rho u is the transpose of &minus &rho u for all u in math mathfrak g math . Overline &rho is also a representation, as can be explicitly checked. For a unitary representation , the conjugate representation and the dual representation coincide, up to equivalence of representations. Generalization A general ring Module mathematics module does not admit a dual representation. Modules of Hopf algebra s do, however. See also Complex conjugate representation Kirillov Character Formula References references Category Representation theory of groups fr Repr sentation duale ... more details
In mathematics , representation is a very general relationship that expresses similarities between objects. Roughly speaking, a collection Y of mathematical objects may be said to represent another collection X of objects, provided that the properties and relationships existing among the representing objects y sub i sub conform in some consistent way to those existing among the corresponding represented objects x sub i sub . Somewhat more formally, for a set of properties and relation mathematics relations , a representation of some structure X is a structure Y that is the image of X under an isomorphism that preserves . The label representation is sometimes also applied to the isomorphism itself. Representation theory Perhaps the most well developed example of this general notion is the subfield of abstract algebra called representation theory , which studies the representing of elements of algebraic structures by linear transformations of vector spaces . Other examples Although the termrepresentation theory is well established in the algebraic sense discussed above, there are many other uses of the termrepresentation throughout mathematics. Graph theory An active area of graph theory is the exploration of isomorphisms between graph mathematics graphs and other structures. A key class of such problems stems from the fact that, like adjacency relation adjacency in undirected ... title The representation of a graph by set intersections journal Canadian Journal of Mathematics volume ... to tell us this phenomenon is called polysemy , a polysemy term borrowed from linguistics . Examples ... first Paul J. title Simultaneous intersection representation of pairs of graphs journal Journal of Graph ... intervals that is an interval order representation of P sub 1 sub and an interval containment representation of P sub 2 sub . ref citation last Tanenbaum first Paul J. title Simultaneous representation ... 1996 pages 339&ndash 350 id MathSciNet id 1452517 doi 10.1007 BF00405593 ref See also Representation ... more details
Unreferenced date December 2009 Orphan date December 2009 This article addresses the notion of quasiregularity in the context of representation theory and topological algebra . For other notions of quasiregularity in mathematics , see the disambiguation page quasiregular . In mathematics, quasiregular representation is a concept of representation theory, for a locally compact group G and a homogeneous space G H where H is a closed subgroup . In line with the concepts of regular representation and induced representation , G acts on functions on G H . If however Haar measure s give rise only to a quasi invariant measure on G H , certain correction factors have to be made to the action on functions, for L sup 2 sup G H to afford a unitary representation of G on square integrable function s. With appropriate scaling factors, therefore, introduced into the action of G , this is the quasiregular representation or modified induced representation. DEFAULTSORT Quasiregular Representation Category Unitary representation theory Category Topological groups ... more details
distinguish Trivial module In the mathematics mathematical field of representation theory , a trivial representation is a group representationrepresentation math V , &phi of a Group mathematics group G on which all elements of G act as the identity mapping of V . A trivial Representation mathematics representation of an associative algebra associative or Lie algebra is a Lie algebra representation Lie algebra representation for which all elements of the algebra act as the zero linear map endomorphism which sends every element of V to the zero vector . For any group or Lie algebra, an irreducible representation irreducible trivial representation always exists over any field, and is one dimensional, hence unique up to isomorphism. The same is true for associative algebras unless one restricts attention to unital algebra s and unital representations. Although the trivial representation is constructed in such a way as to make its properties seem tautologous, it is a fundamental object of the theory. A subrepresentation is equivalent to a trivial representation, for example, if it consists of invariant vectors so that searching for such subrepresentations is the whole topic of invariant theory . The trivial character is the character mathematics character that takes the value of one for all group elements. References Fulton Harris . Category Representation theory algebra stub zh ... more details
Multiple issues orphan March 2012 context February 2012 unreferenced February 2012 Politics Models of representation refer to ways in which elected officials behave in representative democracy representative democracies . There are three types delegate , trustee , and politician politico . See also Delegate model of representation Trustee model of representation Category Democracy ... more details
In mathematics , in the representation theory of algebraic group s, a linear representation of an algebraic group is said to be rational if, viewed as a map from the group to the general linear group, it is a rational map of algebraic varieties. Finite direct sums and products of rational representations are rational. A rational math G math module is a module that can be expressed as a sum not necessarily direct of rational representations. see Group representation References http www.jstor.org view 00029327 di994362 99p00143 Extensions of Representations of Algebraic Linear Groups http www.encyclopediaofmath.org index.php Rational representation Springer Online Reference Works Rational Representation Category Representation theory of algebraic groups algebra stub ... more details
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