householder

Scilab Function
Last update : 25/04/2007

householder - Householder orthogonal reflexion matrix

### Calling Sequence

  `u=householder(v [,w])`

### Parameters

- `v` : real or complex column vector
- `w` : real or complex column vector with same size as `v` . Default value is `eye(v)`
- `u` : real or complex column vector

### Description

given 2 column vectors `v` , `w` of same size, `householder(v,w)` returns a unitary column vector `u` , such that `(eye()-2*u*u')*v` is proportional to `w` . `(eye()-2*u*u')` is the orthogonal Householder reflexion matrix .

`w` default value is `eye(v)` . In this case vector `(eye()-2*u*u')*v` is the vector `eye(v)*norm(v)` .

### See Also

`qr` , `givens` ,