title: Semisimple element
text: # Semisimple element
  
  In mathematics, a semisimple element is an abstract element of an algebraic structure that generalizes a diagonalizable matrix. A precise meaning depends on 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 image under the adjoint representation is semisimple; see Semisimple Lie algebra#Jordan decomposition.
  