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Representation Of A Lie Algebra
Representation may refer to: Law and politics *Representation (politics), political activities undertaken by elected representatives, as well as other theories ** Representative democracy, type of democracy in which elected officials represent a group of people * Representation in contract law, a pre-contractual statement that may (if untrue) result in liability for misrepresentation * Labor representation, or worker representation, the work of a union representative who represents and defends the interests of fellow labor union members * Legal representation, provided by a barrister, lawyer, or other advocate * Lobbying or interest representation, attempts to influence the actions, policies, or decisions of officials * " No taxation without representation", a 1700s slogan that summarized one of the American colonists' 27 colonial grievances in the Thirteen Colonies, which was one of the major causes of the American Revolution * Permanent representation, a type of diplomatic missio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Representation (politics)
Political representation is the activity of making citizens "present" in public policy-making processes when political actors act in the best interest of citizens according to Hanna Pitkin, Hanna Pitkin's ''Concept of Representation'' (1967). This definition of political representation is consistent with a wide variety of views on what representing implies and what the duties of representatives are. For example, representing may imply acting on the expressed wishes of citizens, but it may alternatively imply acting according to what the representatives themselves judge is in the best interests of citizens. And representatives may be viewed as individuals who have been authorized to act on the behalf of others, or may alternatively be viewed as those who will be held to account by those they are representing. Political representation can happen along different units such as social groups and area, and there are different types of representation such as substantive representation an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Representation Theory (linguistics)
Representation theory (RT) is a theoretical linguistic framework in the generative tradition, created and developed by Edwin S. Williams – chiefly in an eponymous monograph of 2003. Williams compares it with other frameworks such as Noam Chomsky's minimalist program, and argues that his proposal has significant descriptive and conceptual advantages over them. The substance of the proposal is that linguistic derivation is the result of mappings and mismappings between an open set of 'representations', which in one dimension correspond to increasingly larger locality domains and in the other pair ' syntactic' (sentential and sub-sentential) and 'semantic' (as well as pragmatic) levels. Cross-linguistic variation is then accounted for by the prioritisation of 'faithfulness' to some representations over others. See also * Discourse representation theory References External linksEdwin S. Williamsat Princeton University Princeton University is a private university, pri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Visualization
Data and information visualization (data viz/vis or info viz/vis) is the practice of designing and creating Graphics, graphic or visual Representation (arts), representations of a large amount of complex quantitative and qualitative data and information with the help of static, dynamic or interactive visual items. Typically based on data and information collected from a certain domain of expertise, these visualizations are intended for a broader audience to help them visually explore and discover, quickly understand, interpret and gain important insights into otherwise difficult-to-identify structures, relationships, correlations, local and global patterns, trends, variations, constancy, clusters, outliers and unusual groupings within data (''exploratory visualization''). When intended for the general public (mass communication) to convey a concise version of known, specific information in a clear and engaging manner (''presentational'' or ''explanatory visualization''), it is t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Representative Sample
In this statistics, quality assurance, and survey methodology, sampling is the selection of a subset or a statistical sample (termed sample for short) of individuals from within a statistical population to estimate characteristics of the whole population. The subset is meant to reflect the whole population, and statisticians attempt to collect samples that are representative of the population. Sampling has lower costs and faster data collection compared to recording data from the entire population (in many cases, collecting the whole population is impossible, like getting sizes of all stars in the universe), and thus, it can provide insights in cases where it is infeasible to measure an entire population. Each observation measures one or more properties (such as weight, location, colour or mass) of independent objects or individuals. In survey sampling, weights can be applied to the data to adjust for the sample design, particularly in stratified sampling. Results from probab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Social Representation
Social representations are a system of values, ideas, metaphors, beliefs, and practices that serve to establish social order, orient participants and enable communication among the members of groups and communities. Social representation theory is a body of theory within social psychology and sociological social psychology. It has parallels in sociological theorizing such as social constructionism and symbolic interactionism, and is similar in some ways to mass consensus and discursive psychology. Origin and definition The term ''social representation'' was originally coined by Serge Moscovici in 1961,Moscovici, S. (1961). ''La psychanalyse, son image et son public''. Paris: Presses Universitaires de France. in his study on the reception and circulation of psychoanalysis in France. It is understood as the collective elaboration "of a social object by the community for the purpose of behaving and communicating". They are further referred to as "system of values, ideas and practice ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Representation (chemistry)
The structural formula of a chemical compound is a graphic representation of the molecular structure (determined by structural chemistry methods), showing how the atoms are connected to one another. The chemical bonding within the molecule is also shown, either explicitly or implicitly. Unlike other chemical formula types, which have a limited number of symbols and are capable of only limited descriptive power, structural formulas provide a more complete geometric representation of the molecular structure. For example, many chemical compounds exist in different isomeric forms, which have different enantiomeric structures but the same molecular formula. There are multiple types of ways to draw these structural formulas such as: Lewis structures, condensed formulas, skeletal formulas, Newman projections, Cyclohexane conformations, Haworth projections, and Fischer projections. Several systematic chemical naming formats, as in chemical databases, are used that are equivalent to, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiple Representations (mathematics Education)
In mathematics education, a representation is a way of encoding an idea or a relationship, and can be both internal (e.g., mental construct) and external (e.g., graph). Thus multiple representations are ways to symbolize, to describe and to refer to the same mathematical entity. They are used to understand, to develop, and to communicate different mathematical features of the same object or operation, as well as connections between different properties. Multiple representations include graphs and diagrams, tables and grids, formulas, symbols, words, gestures, software code, videos, concrete models, physical and virtual manipulatives, pictures, and sounds. Representations are thinking tools for doing mathematics. Higher-order thinking The use of multiple representations supports and requires tasks that involve decision-making and other problem-solving skills.S. Ainsworth, P. Bibby, and D. Wood, "Information technology and multiple representations: New opportunities – new problems ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lie Algebra Representation
In the mathematical field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices (or endomorphisms of a vector space) in such a way that the Lie bracket is given by the commutator. In the language of physics, one looks for a vector space V together with a collection of operators on V satisfying some fixed set of commutation relations, such as the relations satisfied by the angular momentum operators. The notion is closely related to that of a representation of a Lie group. Roughly speaking, the representations of Lie algebras are the differentiated form of representations of Lie groups, while the representations of the universal cover of a Lie group are the integrated form of the representations of its Lie algebra. In the study of representations of a Lie algebra, a particular ring, called the universal enveloping algebra, associated with the Lie algebra plays an important role. The u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Representation Of A Lie Group
In mathematics and theoretical physics, a representation of a Lie group is a linear action of a Lie group on a vector space. Equivalently, a representation is a smooth homomorphism of the group into the group of invertible operators on the vector space. Representations play an important role in the study of continuous symmetry. A great deal is known about such representations, a basic tool in their study being the use of the corresponding 'infinitesimal' representations of Lie algebras. Finite-dimensional representations Representations A complex representation of a group is an action by a group on a finite-dimensional vector space over the field \mathbb C. A representation of the Lie group ''G'', acting on an ''n''-dimensional vector space ''V'' over \mathbb C is then a smooth group homomorphism :\Pi:G\rightarrow\operatorname(V), where \operatorname(V) is the general linear group of all invertible linear transformations of V under their composition. Since all ''n''-dimensi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group Representation
In the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to itself (i.e. vector space automorphisms); in particular, they can be used to represent group elements as invertible matrices so that the group operation can be represented by matrix multiplication. In chemistry, a group representation can relate mathematical group elements to symmetric rotations and reflections of molecules. Representations of groups allow many group-theoretic problems to be reduced to problems in linear algebra. In physics, they describe how the symmetry group of a physical system affects the solutions of equations describing that system. The term ''representation 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" means a homomorphism from the group to the autom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Representation (mathematics)
In mathematics, a representation is a very general relationship that expresses similarities (or equivalences) between mathematical objects or structures. 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 ''yi'' conform, in some consistent way, to those existing among the corresponding represented objects ''xi''. More specifically, given a set ''Π'' of properties and relations, a ''Π''-representation of some structure ''X'' is a structure ''Y'' that is the image of ''X'' under a homomorphism that preserves ''Π''. The label ''representation'' is sometimes also applied to the homomorphism itself (such as group homomorphism in group theory). Representation theory Perhaps the most well-developed example of this general notion is the subfield of abstract algebra called representation theory, which studies the representin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knowledge Representation
Knowledge representation (KR) aims to model information in a structured manner to formally represent it as knowledge in knowledge-based systems whereas knowledge representation and reasoning (KRR, KR&R, or KR²) also aims to understand, reason, and interpret knowledge. KRR is widely used in the field of artificial intelligence (AI) with the goal to represent information about the world in a form that a computer system can use to solve complex tasks, such as diagnosing a medical condition or having a natural-language dialog. KR incorporates findings from psychology about how humans solve problems and represent knowledge, in order to design formalisms that make complex systems easier to design and build. KRR also incorporates findings from logic to automate various kinds of ''reasoning''. Traditional KRR focuses more on the declarative representation of knowledge. Related knowledge representation formalisms mainly include vocabularies, thesaurus, semantic networks, axiom system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
