INSTITUTE OF INFORMATION TECHNOLOGIES - BAS

Cybernetics and Information Technologies
Volume 4, No 2. Sofia, 2004, Bulgarian Academy of Sciences


A Criterion for Reducibility of Matrices

Vladimir Monov1, Michael Tsatsomeros2

1 Institute of Information Technologies, 1113 Sofia
E-mail: vmonov@iit.bas.bg
2 Mathematics Department, Washington State University, Pullman, WA 99164-3113, USA
E-mail: tsat@math.wsu.edu


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.