矩阵多项式是数学中矩阵论里的概念，指由方块矩阵作为不定元的多项式，或由方块矩阵作为变量的多项式函数。

给定自然数n、系数环以及n阶方块矩阵A，一个关于矩阵A的d次的矩阵多项式通常写作：

其中的都是系数环中的元素。这其实是可以看作将中的多项式：

中的不定元换成了一个n阶方块矩阵A后得到的结果。P(A)和A一样，也是一个n阶方块矩阵。

In mathematics, a matrix polynomial is a polynomial with matrices as variables. Given an ordinary, scalar-valued polynomial

this polynomial evaluated at a matrix A is

where I is the identity matrix.

A matrix polynomial equation is an equality between two matrix polynomials, which holds for the specific matrices in question. A matrix polynomial identity is a matrix polynomial equation which holds for all matrices A in a specified matrix ring M_n(R).