semisimple matrix
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Semisimple module — In mathematics, especially in the area of abstract algebra known as module theory, a semisimple module or completely reducible module is a type of module that can be understood easily from its parts. A ring which is a semisimple module over… … Wikipedia
Matrix ring — In abstract algebra, a matrix ring is any collection of matrices forming a ring under matrix addition and matrix multiplication. The set of n×n matrices with entries from another ring is a matrix ring, as well as some subsets of infinite matrices … Wikipedia
Semisimple algebra — In ring theory, a semisimple algebra is an associative algebra which has trivial Jacobson radical (that is only the zero element of the algebra is in the Jacobson radical). If the algebra is finite dimensional this is equivalent to saying that it … Wikipedia
Semisimple — This article is about mathematical use. For the philosophical reduction thinking, see Reduction (philosophy). In mathematics, the term semisimple (sometimes completely reducible) is used in a number of related ways, within different subjects. The … Wikipedia
Semisimple algebraic group — In mathematics, especially in the areas of abstract algebra and algebraic geometry studying linear algebraic groups, a semisimple algebraic group is a type of matrix group which behaves much like a semisimple Lie algebra or semisimple ring.… … Wikipedia
Diagonalizable matrix — In linear algebra, a square matrix A is called diagonalizable if it is similar to a diagonal matrix, i.e., if there exists an invertible matrix P such that P −1AP is a diagonal matrix. If V is a finite dimensional vector space, then a linear … Wikipedia
Glossary of semisimple groups — This is a glossary for the terminology applied in the mathematical theories of semisimple Lie groups. It also covers terms related to their Lie algebras, their representation theory, and various geometric, algebraic and combinatorial structures… … Wikipedia
Cartan matrix — In mathematics, the term Cartan matrix has two meanings. Both of these are named after the French mathematician Élie Cartan. In an example of Stigler s law of eponymy, Cartan matrices in the context of Lie algebras were first investigated by… … 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
Dynkin diagram — See also: Coxeter–Dynkin diagram Finite Dynkin diagrams Affine (extended) Dynkin diagrams … Wikipedia
Tempered representation — In mathematics, a tempered representation of a linear semisimple Lie group is a representation that has a basis whose matrix coefficients lie in the L p space : L 2+ epsilon;( G ) for any epsilon; gt; 0. FormulationThis condition, as just given,… … Wikipedia
