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In mathematics, a polynomial matrix or matrix of polynomials is a matrix whose elements are univariate or multivariate polynomials. Equivalently, a polynomial matrix is a polynomial whose coefficients are matrices.
A univariate polynomial matrix P of degree p is defined as:
where A {\displaystyle A} denotes a matrix of constant coefficients, and A {\displaystyle A} is non-zero. An example 3×3 polynomial matrix, degree 2:
We can express this by saying that for a ring R, the rings M n ] {\displaystyle M_{n}]} and ] {\displaystyle ]} are isomorphic.
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