compute the Jordan form of a matrix
(optional) used to return the transition matrix
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=diag⁡j1,j2,...,jk 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 inverse⁡P⁢A⁢P=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.
A ≔ matrix⁡2,2,1,0,3,2
J ≔ jordan⁡A,'P'
evalm⁡P−1 &* A &* P
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