Necessary and sufficient Condition For Existence a k-dimension A-coninvariant Subspace of Cn

Necessary and sufficient Condition For Existence a k-dimension A-coninvariant Subspace of Cn

We know  is a coneigenvalue of a matrix A 2 Cnn if there exists a nonzero vector x 2 Cn such that Ax = x. Coneigenvalues dened in this way may exist if and only if AA has real nonnegative (ordinary) eigenvalues. If A does have coneigenvalues, there are always innitely many of them. We attempt a number of new facts on coninvariant subspaces and block tri- angular matrices consimilarity with them. In this paper, we show that each square matrix is consimilar with block triangular matrix if and only if has a nontrivial A-coninvariant sub- space.