A binomial-like matrix equation

Alin Bostan (1) , Thierry Combot (2)

1 SPECFUN - Symbolic Special Functions : Fast and Certified
2 IMCCE - Institut de Mécanique Céleste et de Calcul des Ephémérides

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.

Domaines: Mathématiques générales [math.GM]; Physique [physics]; Astrophysique [astro-ph]

Alin Bostan, Thierry Combot. A binomial-like matrix equation. The American Mathematical Monthly, 2012, 119 (7), pp.593-597. ⟨10.4169/amer.math.monthly.119.07.593⟩. ⟨hal-00780438⟩