A polynomial with matrix coefficients. An 
th order matrix polynomial in a variable 
is given by
 |
where 
are 
square matrices.
Matrix Polynomial
See also
Cayley-Hamilton Theorem, Matrix Power, Nilpotent Matrix, Polynomial MatrixExplore with Wolfram|Alpha
References
Edelman, A. and Kostlan, E. "How Many Zeros of a Random Polynomial are Real?" Bull. Amer. Math. Soc. 32, 1-37, 1995.Faddeeva, V. N. Computational Methods of Linear Algebra. New York: Dover, p. 13, 1958.Referenced on Wolfram|Alpha
Matrix PolynomialCite this as:
Weisstein, Eric W. "Matrix Polynomial." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MatrixPolynomial.html