jordan - Compute Jordan canonical form of matrix
Syntax
J = jordan(A)
[V, J] = jordan(A)
Description
J = jordan(A) computes the Jordan canonical
(normal) form of a symbolic or numeric matrix A.
The Jordan form of a numeric matrix is extremely sensitive to numerical
errors. To compute Jordan canonical form of a matrix, represent the
elements of the matrix by integers or ratios of small integers, if
possible.
[V, J] = jordan(A) computes the Jordan
canonical form J and the similarity transform V.
The matrix V contains the generalized eigenvectors
of A as columns, and V\A*V = J.
Examples
Compute the Jordan canonical form and the similarity transform
for the following numeric matrix. Verify that the resulting matrix V satisfies
the condition V\A*V = J:
A = [1 -3 -2; -1 1 -1; 2 4 5]
[V, J] = jordan(A)
V\A*V
The result is:
A =
1 -3 -2
-1 1 -1
2 4 5
V =
-1 1 -1
-1 0 0
2 0 1
J =
2 1 0
0 2 0
0 0 3
ans =
2 1 0
0 2 0
0 0 3See Also
eig | inv | poly
 | jacobian | | lambertw (sym) |  |
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