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jordan

Jordan form of matrix

Syntax

J = jordan(A)
[V,J] = jordan(A)

Description

J = jordan(A) computes the Jordan canonical form (also called Jordan 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 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 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 form and the similarity transform for this 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
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     3

Introduced before R2006a

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