Jump to content

Matrix polynomial

From Wikipedia, the free encyclopedia
This is an old revision of this page, as edited by 70.114.144.248 (talk) at 02:48, 29 September 2013 (Removed irrelevant definition of matrix commutator.). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

In mathematics, a matrix polynomial is a polynomial with matrices as variables. Examples include:

where P is a polynomial,
and I is the identity matrix.

A matrix polynomial equation is an equality between two matrix polynomials, which holds for the specific matrices in question. If , (where A is a matrix over a field), then the eigenvalues of A satisfy the characteristic equation[disputeddiscuss] .
A matrix polynomial identity is a matrix polynomial equation which holds for all matricies A in a specified matrix ring Mn(R).