Campus Livre
polyvalm
Evaluates a polynomial with a square matrix as the variable.
Category: Mathematics > Elementary Math
Syntax
Y = polyvalm(p, X)Evaluates p(1)*X^n + ... + p(n)*I using matrix products.
Description
Where polyval squares each entry, polyvalm uses true matrix powers, and the constant term is multiplied by the identity matrix. The Cayley-Hamilton theorem says that a matrix annihilates its own characteristic polynomial, so polyvalm(poly(A), A) is the zero matrix, up to rounding.
Input arguments
p- Coefficient vector, highest power first.
X- Square matrix.
Output arguments
Y- Square matrix of the same size as
X.
Example
Matrix polynomial
A = [1 2; 3 4];
polyvalm([1 0 1], A)
A^2 + eye(2)Output
ans = 2×2
8 10
15 23
ans = 2×2
8 10
15 23