Matrix polynomial
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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[disputed – discuss] .
A matrix polynomial identity is a matrix polynomial equation which holds for all matricies A in a specified matrix ring Mn(R).