linear operator T : V → V on a vector space V is semisimple if every T-invariant subspace has a complementary T-invariant subspace. If T is a semisimple linear...

irreducible) if the only invariant subspaces for those operators are zero and the vector space itself; a semisimple representation then is a direct sum of simple...

context: A semisimple element in the endomorphism ring of a vector space is a semisimple operator. In a semisimple Lie algebra, an element is semisimple if its...

diagonalisable part is also characterised as the semisimple part. A basic question in linear algebra is whether an operator on a finite-dimensional vector space can...

generally ladder operators can be understood in the context of a root system of a semisimple Lie group and the associated semisimple Lie algebra without...

finite-dimensional representation of a semisimple compact Lie group is semisimple. A square matrix (in other words a linear operator T : V → V {\displaystyle T:V\to...

In mathematics, a Lie algebra is semisimple if it is a direct sum of simple Lie algebras. (A simple Lie algebra is a non-abelian Lie algebra without any...

be completely reducible (or semisimple) if it is isomorphic to a direct sum of irreducible representations (cf. semisimple module). If V is finite-dimensional...

Jacobson semisimple ring or J-semisimple ring is a ring whose Jacobson radical is zero. This is a type of ring more general than a semisimple ring, but...

a diagonalizable (semisimple) operator corresponds to a reduced variety; a cyclic module (one generator) corresponds to the operator having a cyclic vector...