Cramer and Cayley-Hamilton in the max algebra

The Cayley–Hamilton Theorem

The Cayley-Hamilton theorem

Theorem 1. Let A be a n × n matrix, and let p(λ) = det(λI − A) be the characteristic polynomial of A. Then p(A) = 0.

The Cayley-Hamilton Theorem

This document contains a proof of the Cayley-Hamilton theorem based on the development of matrices in HOL/Multivariate Analysis.

Cayley-Hamilton Theorem

Generalized Cayley-Hamilton-Newton identities

The q-generalizations of the two fundamental statements of matrix algebra – the Cayley-Hamilton theorem and the Newton relations – to the cases of quantum matrix algebras of an ”RTT-” and of a ”Reflection equation” types have been obtained in [2]–[6]. We construct a family of matrix identities which we call Cayley-HamiltonNewton identities and which underlie the characteristic identity as well ...