## McCoy's Theorem

If two Square Matrices A and B are simultaneously upper triangularizable by similarity transforms, then there is an ordering , ..., of the Eigenvalues of A and , ..., of the Eigenvalues of B so that, given any Polynomial in noncommuting variables, the Eigenvalues of are the numbers with , ..., . McCoy's theorem states the converse: If every Polynomial exhibits the correct Eigenvalues in a consistent ordering, then A and B are simultaneously triangularizable.

References

Luchins, E. H. and McLoughlin, M. A. In Memoriam: Olga Taussky-Todd.'' Not. Amer. Math. Soc. 43, 838-847, 1996.