poly - Maple Help

MTM

 poly
 compute the characteristic polynomial of a matrix

 Calling Sequence poly(A) poly(A,x)

Parameters

 A - matrix, vector, array, or scalar x - (optional) name

Description

 • The function poly(A,x) returns the characteristic polynomial in x that has the eigenvalues of the matrix A as its roots (all multiplicities respected).
 • This polynomial is the determinant of x*I - A, where I is the identity matrix with the dimension of A.
 • If the parameter x is omitted, then the name x is used.

Examples

 > $\mathrm{with}\left(\mathrm{MTM}\right):$
 > $A≔\mathrm{Matrix}\left(\left[\left[1,2,1\right],\left[2,4,2\right],\left[2,8,1\right]\right]\right)$
 ${A}{≔}\left[\begin{array}{ccc}{1}& {2}& {1}\\ {2}& {4}& {2}\\ {2}& {8}& {1}\end{array}\right]$ (1)
 > $\mathrm{poly}\left(A\right)$
 ${{x}}^{{3}}{-}{6}{}{{x}}^{{2}}{-}{13}{}{x}$ (2)
 > $\mathrm{poly}\left(A,'z'\right)$
 ${{z}}^{{3}}{-}{6}{}{{z}}^{{2}}{-}{13}{}{z}$ (3)