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Journal Article

A Binomial-like Matrix Equation

Alin Bostan and Thierry Combot
The American Mathematical Monthly
Vol. 119, No. 7 (August‒September 2012), pp. 593-597
DOI: 10.4169/amer.math.monthly.119.07.593
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.119.07.593
Page Count: 5

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Topics: Eigenvalues, Matrices, Polynomials, Algebra, Mathematical problems, Spectral theory, Eigenvectors
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A Binomial-like Matrix Equation
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Abstract

Abstract We show that a pair of matrices satisfying a certain algebraic identity, reminiscent of the binomial theorem, must have the same characteristic polynomial. This is a generalization of Problem 4 (11th grade) from the Romanian National Mathematical Olympiad 2011.

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