Now showing items 1-1 of 1

  • Canonical forms for families of anti-commuting diagonalizable linear operators 

    Authors:Kumbasar, Yalcin; Bilge, Ayşe Hümeyra
    Publisher and Date:(Elsevier Science Inc, 2012)
    It is well known that a commuting family of diagonalizable linear operators on a finite dimensional vector space is simultaneously diagonalizable. In this paper we consider a family A = {A(a)} A(a) : V -> V a = 1... N of anti-commuting (complex) linear operators on a finite dimensional vector space. We prove that if the family is diagonalizable over the complex numbers then V has an A-invariant direct sum decomposition into subspaces V(alpha) such that the restriction of the family A to V(alpha) ...