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# rowshuff

shuffle algorithm

### Syntax

[Ws,Fs1]=rowshuff(Fs, [alfa])

### Arguments

- Fs
square real pencil

`Fs = s*E-A`

- Ws
polynomial matrix

- Fs1
square real pencil

`F1s = s*E1 -A1`

with`E1`

non-singular- alfa
real number (

`alfa = 0`

is the default value)

### Description

Shuffle algorithm: Given the pencil `Fs=s*E-A`

, returns Ws=W(s)
(square polynomial matrix) such that:

`Fs1 = s*E1-A1 = W(s)*(s*E-A)`

is a pencil with non singular `E1`

matrix.

This is possible iff the pencil `Fs = s*E-A`

is regular (i.e. invertible).
The degree of `Ws`

is equal to the index of the pencil.

The poles at infinity of `Fs`

are put to `alfa`

and the zeros of `Ws`

are at `alfa`

.

Note that `(s*E-A)^-1 = (s*E1-A1)^-1 * W(s) = (W(s)*(s*E-A))^-1 *W(s)`

## Comments

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