McCoy's Theorem
If two Square 
Matrices A and B are simultaneously uppertriangularizable by similarity transforms, then there is an ordering 
, ..., 
of theEigenvalues of A and 
, ..., 
of the Eigenvalues of B so that,given any Polynomial 
in noncommuting variables, the Eigenvalues of 
are thenumbers 
with 
, ..., 
. McCoy's theorem states the converse: If every Polynomial exhibits thecorrect Eigenvalues in a consistent ordering, then A and B are simultaneouslytriangularizable.
References
Luchins, E. H. and McLoughlin, M. A. ``In Memoriam: Olga Taussky-Todd.'' Not. Amer. Math. Soc. 43, 838-847, 1996.
- Absolute Deviation
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- Adams-Bashforth-Moulton Method
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