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linalg(deprecated)

 jordan
 compute the Jordan form of a matrix

 Calling Sequence jordan(A) jordan(A, 'P')

Parameters

 A - square matrix 'P' - (optional) used to return the transition matrix

Description

 • 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.

Examples

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

 > $\mathrm{with}\left(\mathrm{linalg}\right):$
 > $A≔\mathrm{matrix}\left(2,2,\left[1,0,3,2\right]\right)$
 ${A}{≔}\left[\begin{array}{cc}{1}& {0}\\ {3}& {2}\end{array}\right]$ (1)
 > $J≔\mathrm{jordan}\left(A,'P'\right)$
 ${J}{≔}\left[\begin{array}{cc}{1}& {0}\\ {0}& {2}\end{array}\right]$ (2)
 > $\mathrm{print}\left(P\right)$
 $\left[\begin{array}{cc}{1}& {0}\\ {-3}& {3}\end{array}\right]$ (3)
 > $\mathrm{evalm}\left(\left({P}^{-1}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&*\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}A\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&*\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}P\right)$
 $\left[\begin{array}{cc}{1}& {0}\\ {0}& {2}\end{array}\right]$ (4)

 See Also