# 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```

## See Also

#### Introduced before R2006a

Was this topic helpful?

Get trial now