# Common Invariant Subspace and Commuting Matrices

@article{Bourgeois2012CommonIS,
title={Common Invariant Subspace and Commuting Matrices},
author={G. Bourgeois},
journal={arXiv: Rings and Algebras},
year={2012}
}
• G. Bourgeois
• Published 2012
• Mathematics
• arXiv: Rings and Algebras
• Let $K$ be a perfect field, $L$ be an extension field of $K$ and $A,B\in\mathcal{M}_n(K)$. If $A$ has $n$ distinct eigenvalues in $L$ that are explicitly known, then we can check if $A,B$ are simultaneously triangularizable over $L$. Now we assume that $A,B$ have a common invariant proper vector subspace of dimension $k$ over an extension field of $K$ and that $\chi_A$, the characteristic polynomial of $A$, is irreducible over $K$. Let $G$ be the Galois group of $\chi_A$. We show the following… CONTINUE READING
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