A Criterion for Reducibility of Matrices
Vladimir Monov1, Michael Tsatsomeros2
1 Institute of Information Technologies, 1113 Sofia
2 Mathematics Department, Washington State University, Pullman, WA 99164-3113, USA
Abstract:The problem of existence and characterization of non-trivial reducing subspaces for a given matrix is studied employing some basic tools of multilinear algebra. A criterion for reducibility of a single matrix is obtained which is also extended to the case of simultaneous reduction of two or more matrices.
Keywords: reducing subspace, invariant subspace, compound matrix, Grassmann space, decomposable vector.