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.

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

$A≔\mathrm{Matrix}\left(\left[\left[1\,2\,1\right]\,\left[2\,4\,2\right]\,\left[2\,8\,1\right]\right]\right)$

$A≔\left[\begin{array}{ccc}1& 2& 1\\ 2& 4& 2\\ 2& 8& 1\end{array}\right]$

$\mathrm{poly}\left(A\right)$

$x^3-6x^2-13x$

$\mathrm{poly}\left(A\,'z'\right)$

$z^3-6z^2-13z$