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# bdiag

block diagonalization, generalized eigenvectors

### Syntax

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

### Arguments

- 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

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