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

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

The call jordan(A) computes and returns the Jordan form J of a matrix A.

J has the following structure: $J=\mathrm{diag}\left(\mathrm{j1},\mathrm{j2},...,\mathrm{jk}\right)$ where the ji's are Jordan block matrices.  The diagonal entries of these Jordan blocks are the eigenvalues of A (and also of J).

If the optional second argument is given, then P will be assigned the transformation matrix corresponding to this Jordan form, that is, the matrix P such that $\mathrm{inverse}\left(P\right)AP=J$.

The Jordan form is unique up to permutations of the Jordan blocks.

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

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

$A≔\mathrm{matrix}\left(2\,2\,\left[1\,0\,3\,2\right]\right)$

$A≔\left[\begin{array}{cc}1& 0\\ 3& 2\end{array}\right]$

$J≔\mathrm{jordan}\left(A\,'P'\right)$

$J≔\left[\begin{array}{cc}1& 0\\ 0& 2\end{array}\right]$

$\mathrm{print}\left(P\right)$

$\left[\begin{array}{cc}1& 0\\ \mathrm{-3}& 3\end{array}\right]$

$\mathrm{evalm}\left(\left(P^{-1}\&*A\right)\&*P\right)$

$\left[\begin{array}{cc}1& 0\\ 0& 2\end{array}\right]$