householder
===========

Householder orthogonal reflexion matrix



Calling Sequence
~~~~~~~~~~~~~~~~


::

    u=householder(v [,w])




Arguments
~~~~~~~~~

: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`_ QR decomposition
+ `givens`_ Givens transformation


.. _givens: givens.html
.. _qr: qr.html