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.

• Functional
• Functional Analysis
• Functional Calculus
• Functional Derivative
• Function Field
• Function Space
• Functor
• Fundamental Class
• Fundamental Continuity Theorem
• Fundamental Discriminant
• Fundamental Forms
• Fundamental Group
• Fundamental Homology Class
• Fundamental Lemma of Calculus of Variations
• Fundamental System
• Fundamental Theorem of Algebra
• Fundamental Theorem of Arithmetic
• Fundamental Theorem of Curves
• Fundamental Theorem of Directly Similar Figures
• Fundamental Theorem of Gaussian Quadrature
• Fundamental Theorem of Genera
• Fundamental Theorem of Plane Curves
• Fundamental Theorem of Projective Geometry
• Fundamental Theorem of Space Curves
• Fundamental Theorem of Symmetric Functions