Important: The linalg package has been deprecated. Use the superseding command, LinearAlgebra[MinimalPolynomial], instead.

- For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.

The procedure minpoly(A, x) computes the minimum polynomial of the matrix A in x. The minimum polynomial is the polynomial of lowest degree which annihilates A.

The minimum polynomial will always divide the characteristic polynomial.

The command with(linalg,minpoly) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{linalg}\right)\:$

$A≔\mathrm{array}\left(\left[\left[2\,1\,0\,0\right]\,\left[0\,2\,0\,0\right]\,\left[0\,0\,1\,1\right]\,\left[0\,0\,-2\,4\right]\right]\right)\:$

$m≔\mathrm{minpoly}\left(A\,x\right)$

$m≔x^3-7x^2+16x-12$

$p≔\mathrm{expand}\left(\mathrm{charpoly}\left(A\,x\right)\right)$

$p≔x^4-9x^3+30x^2-44x+24$

$\mathrm{divide}\left(p\,m\right)$

$\mathrm{true}$