complex representation

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• Complex representation — 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… …   Wikipedia

• Complex conjugate representation — In mathematics, if G is a group and ρ is a representation of it over the complex vector space V, then the complex conjugate representation ρ* is defined over the conjugate vector space V* as follows: ρ*(g) is the conjugate of ρ(g) for all g in G …   Wikipedia

• Representation ring — In mathematics, especially in the area of algebra known as representation theory, the representation ring of a group is a ring formed from all the (isomorphism classes of the) linear representations of the group. For a given group, the ring will… …   Wikipedia

• Complex system biology — Complex systems biology (CSB) is a branch or subfield of mathematical and theoretical biology concerned with complexity of both structure and function in biological organisms, as well as the emergence and evolution of organisms and species, with… …   Wikipedia

• Representation (arts) — Representation describes the signs that stand in for and take the place of something else.Mitchell, W. 1995, Representation , in F Lentricchia T McLaughlin (eds), Critical Terms for Literary Study , 2nd edn, University of Chicago Press, Chicago]… …   Wikipedia

• representation — refers to the way in which images and texts reconstruct, rather than reflect, the original sources they represent. Thus a painting, photograph, or written text about a tree is never an actual tree, but the reconstruction of what it seemed to be… …   Dictionary of sociology

• Representation theory of finite groups — In mathematics, representation theory is a technique for analyzing abstract groups in terms of groups of linear transformations. See the article on group representations for an introduction. This article discusses the representation theory of… …   Wikipedia

• Representation theory — This article is about the theory of representations of algebraic structures by linear transformations and matrices. For the more general notion of representations throughout mathematics, see representation (mathematics). Representation theory is… …   Wikipedia

• Complex number — A complex number can be visually represented as a pair of numbers forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the square root of –1. A complex… …   Wikipedia

• Representation of a Lie group — In mathematics and theoretical physics, the idea of a representation of a Lie group plays 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… …   Wikipedia

• Representation theory of SL2(R) — In mathematics, the main results concerning irreducible unitary representations of the Lie group SL2(R) are due to Gelfand and Naimark (1946), V. Bargmann (1947), and Harish Chandra (1952). Structure of the complexified Lie algebra We choose a… …   Wikipedia