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.

© 1996-9

1999-05-26