householder

Scilab Function
Last update : April 1993

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`,