matrix realization of group

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• Group theory — is a mathematical discipline, the part of abstract algebra that studies the algebraic structures known as groups. The development of group theory sprang from three main sources: number theory, theory of algebraic equations, and geometry. The… …   Wikipedia

• Group representation — In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group… …   Wikipedia

• Metaplectic group — In mathematics, the metaplectic group Mp2n is a double cover of the symplectic group Sp2n. It can be defined over either real or p adic numbers. The construction covers more generally the case of an arbitrary local or finite field, and even the… …   Wikipedia

• Generalized permutation matrix — In mathematics, a generalized permutation matrix (or monomial matrix) is a matrix with the same nonzero pattern as a permutation matrix, i.e. there is exactly one nonzero entry in each row and each column. Unlike a permutation matrix, where the… …   Wikipedia

• Affine group — In mathematics, the affine group or general affine group of any affine space over a field K is the group of all invertible affine transformations from the space into itself.It is a Lie group if K is the real or complex field or… …   Wikipedia

• Projective unitary group — In mathematics, the projective unitary group PU( n ) is the quotient of the unitary group U( n ) by the right multiplication of its center, U(1), embedded as scalars.Abstractly, it is the isometry group of complex projective space, just as the… …   Wikipedia

• Character theory — This article refers to the use of the term character theory in mathematics. For the media studies definition, see Character theory (Media). In mathematics, more specifically in group theory, the character of a group representation is a function… …   Wikipedia

• Orientation entanglement — In mathematics and physics, the notion of orientation entanglement is sometimes[1] used to develop intuition relating to the geometry of spinors or alternatively as a concrete realization of the failure of the special orthogonal groups to be… …   Wikipedia

• algebra — /al jeuh breuh/, n. 1. the branch of mathematics that deals with general statements of relations, utilizing letters and other symbols to represent specific sets of numbers, values, vectors, etc., in the description of such relations. 2. any of… …   Universalium

• Christianity — /kris chee an i tee/, n., pl. Christianities. 1. the Christian religion, including the Catholic, Protestant, and Eastern Orthodox churches. 2. Christian beliefs or practices; Christian quality or character: Christianity mixed with pagan elements; …   Universalium

• Pauli matrices — The Pauli matrices are a set of 2 times; 2 complex Hermitian and unitary matrices. Usually indicated by the Greek letter sigma (σ), they are occasionally denoted with a tau (τ) when used in connection with isospin symmetries. They are::sigma 1 =… …   Wikipedia