Spectral test of reducibility for Matrix tuples
Functional Analysis
2025-09-09 v1
Abstract
If a tuple of matrices has a common invariant subspace, its projective joint spectrum has an algebraic component. In general, the converse is not true, and there might be algebraic components in the projective joint spectrum without corresponding common invariant subspaces. In this paper we give necessary and sufficient conditions for the occurrence of such correspondence.
Cite
@article{arxiv.2509.05836,
title = {Spectral test of reducibility for Matrix tuples},
author = {Michael Stessin and Rongwei Yang},
journal= {arXiv preprint arXiv:2509.05836},
year = {2025}
}
Comments
18 pages