linalg(deprecated)/minpoly - Help

linalg(deprecated)

 minpoly
 compute the minimum polynomial of a matrix

 Calling Sequence minpoly(A, x)

Parameters

 A - square matrix x - name

Description

 • 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.

Examples

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

 > $\mathrm{with}\left(\mathrm{linalg}\right):$
 > $A≔\mathrm{array}\left(\left[\left[2,1,0,0\right],\left[0,2,0,0\right],\left[0,0,1,1\right],\left[0,0,-2,4\right]\right]\right):$
 > $m≔\mathrm{minpoly}\left(A,x\right)$
 ${m}{≔}{{x}}^{{3}}{-}{7}{}{{x}}^{{2}}{+}{16}{}{x}{-}{12}$ (1)
 > $p≔\mathrm{expand}\left(\mathrm{charpoly}\left(A,x\right)\right)$
 ${p}{≔}{{x}}^{{4}}{-}{9}{}{{x}}^{{3}}{+}{30}{}{{x}}^{{2}}{-}{44}{}{x}{+}{24}$ (2)
 > $\mathrm{divide}\left(p,m\right)$
 ${\mathrm{true}}$ (3)