bdiag

Scilab Function
Last update : 25/04/2007

bdiag - block diagonalization, generalized eigenvectors

### Calling Sequence

  `[Ab [,X [,bs]]]=bdiag(A [,rmax])`

### Parameters

- `A` : real or complex square matrix
- `rmax` : real number
- `Ab` : real or complex square matrix
- `X` : real or complex non-singular matrix
- `bs` : vector of integers

### Description

    [Ab [,X [,bs]]]=bdiag(A [,rmax])

performs the block-diagonalization of matrix `A` . bs gives the structure of the blocks (respective sizes of the blocks). `X` is the change of basis i.e `Ab = inv(X)*A*X` is block diagonal.

`rmax` controls the conditioning of `X` ; the default value is the l1 norm of `A` .

To get a diagonal form (if it exists) choose a large value for `rmax` (`rmax=1/%eps` for example). Generically (for real random A) the blocks are (1x1) and (2x2) and `X` is the matrix of eigenvectors.

### Examples

    //Real case: 1x1 and 2x2 blocks
    a=rand(5,5);[ab,x,bs]=bdiag(a);ab
    //Complex case: complex 1x1 blocks
    [ab,x,bs]=bdiag(a+%i*0);ab

### See Also

`schur` , `sylv` , `spec` ,