# A criterion for the existence of common invariant subspaces of matrices

@article{Tsatsomeros2001ACF, title={A criterion for the existence of common invariant subspaces of matrices}, author={M. Tsatsomeros}, journal={Linear Algebra and its Applications}, year={2001}, volume={322}, pages={51-59} }

It is shown that square matrices A and B have a common invariant subspace W of dimension k > 1 if and only if for some scalar s, A C sI and B C sI are invertible and their kth compounds have a common eigenvector, which is a Grassmann representative for W .T he applicability of this criterion and its ability to yield a basis for the common invariant subspace are investigated. © 2001 Elsevier Science Inc. All rights reserved.

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