JordanForm.md

JordanForm

The JordanForm method is an improved version of the JordanForm method from the LinearAlgebra package for computing the Jordan normal form. It returns the correct result when the matrix has parameters.

Calling Sequence

JordanForm(A)

Input

Variable	Description
A	Square matrix

Output

The Jordan form of the input matrix.

Example

with(LinearAlgebra):
with(ParametricMatrixTools):

p := x^5 + x^4 + x^3 + x^2 + x + a:
F := CompanionMatrix(p, x):

# The LinearAlgebra implementation fails with a parameter
LinearAlgebra:-JordanForm(F);
                             ([0 0 0 0 -a])
                             ([1 0 0 0 -1])
    LinearAlgebra:-JordanForm([0 1 0 0 -1])
                             ([0 0 1 0 -1])
                             ([0 0 0 1 -1])

# The ParametricMatrixTools implementation gives the correct result
ParametricMatrixTools:-JordanForm(F);
    [RootOf(_Z^5+_Z^4+_Z^3+_Z^2+_Z+a, index = 1), 0, 0, 0, 0]
    [0, RootOf(_Z^5+_Z^4+_Z^3+_Z^2+_Z+a, index = 2), 0, 0, 0]
    [0, 0, RootOf(_Z^5+_Z^4+_Z^3+_Z^2+_Z+a, index = 3), 0, 0]
    [0, 0, 0, RootOf(_Z^5+_Z^4+_Z^3+_Z^2+_Z+a, index = 4), 0]
    [0, 0, 0, 0, RootOf(_Z^5+_Z^4+_Z^3+_Z^2+_Z+a, index = 5)]