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