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

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

The function charmat constructs the characteristic matrix $M=\mathrm{I}\mathrm{\lambda }-A$, where I is the identity matrix. If lambda is a name, then $\det \left(M\right)$ is the characteristic polynomial.

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

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

$A≔\mathrm{matrix}\left(3\,3\,\left[1\,2\,3\,1\,2\,3\,1\,5\,6\right]\right)$

$A≔\left[\begin{array}{ccc}1& 2& 3\\ 1& 2& 3\\ 1& 5& 6\end{array}\right]$

$\mathrm{charmat}\left(A\,\mathrm{\lambda }\right)$

$\left[\begin{array}{ccc}\mathrm{\lambda }-1& \mathrm{-2}& \mathrm{-3}\\ \mathrm{-1}& \mathrm{\lambda }-2& \mathrm{-3}\\ \mathrm{-1}& \mathrm{-5}& \mathrm{\lambda }-6\end{array}\right]$