MatrixPolynomial
MatrixPolynomial
MatrixPolynomial[{poly,x},m]
evaluates the matrix m at the polynomial poly in the variable x.
MatrixPolynomial[coeffs,m]
evaluates the matrix m at the polynomial whose coefficients are given by coeffs.
Details
- MatrixPolynomial represents a polynomial with square matrices as variables and scalar coefficients.
- MatrixPolynomial[{c0+c1x+⋯+cnxn,x},m] gives
![sum_(i=0)^nc_i MatrixPower[m,i]](Files/MatrixPolynomial.en/1.png "sum_(i=0)^nc_i MatrixPower[m,i]")
. - MatrixPolynomial[{c0,c1,…,cn},m] also gives
![sum_(i=0)^nc_i MatrixPower[m,i]](Files/MatrixPolynomial.en/2.png "sum_(i=0)^nc_i MatrixPower[m,i]")
. - Matrix polynomials occur in the study of matrix algebra such as in the statement of the Cayley–Hamilton theorem, which asserts that MatrixPolynomial[{CharacteristicPolynomial[m,x],x},m] is the zero matrix.
Examples
open all close allScope (1)
Wolfram Research (2025), MatrixPolynomial, Wolfram Language function, https://reference.wolfram.com/language/ref/MatrixPolynomial.html.
Text
Wolfram Research (2025), MatrixPolynomial, Wolfram Language function, https://reference.wolfram.com/language/ref/MatrixPolynomial.html.
CMS
Wolfram Language. 2025. "MatrixPolynomial." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MatrixPolynomial.html.
APA
Wolfram Language. (2025). MatrixPolynomial. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MatrixPolynomial.html