The quantum 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.

The Cayley–Hamilton Theorem

Cayley-Hamilton Theorem

The Cayley-Hamilton Theorem for Noncommutative Semirings

The Cayley-Hamilton theorem (CHT) is a classic result in linear algebra over fields which states that a matrix satisfies its own characteristic polynomial. CHT has been extended from fields to commutative semirings by Rutherford in 1964. However, to the best of our knowledge, no result is known for noncommutative semirings. This is a serious limitation, as the class of regular languages, with f...