From bug-octave-request at bevo dot che dot wisc dot edu Wed Dec 10 12:14:53 2003
Subject: Bad Householder description
From: Vic Norton <vic at norton dot name>
To: <bug-octave at bevo dot che dot wisc dot edu>
Date: Wed, 10 Dec 2003 11:15:31 -0600

Not exactly a bug, but definitely a bad description.

  - Function File: [HOUSV, BETA, ZER] = housh (X, J, Z)
      Computes householder reflection vector housv to reflect x to be
      jth column of identity, i.e., (I - beta*housv*housv')x =e(j) inputs
       x: vector   j: index into vector   z: threshold for zero
      (usually should be the number 0) outputs: (see Golub and Van Loan)
       beta: If beta = 0, then no reflection need be applied (zer set
      to 0)   housv: householder vector

I am sorry, but this description is essentially wrong. Being an
orthogonal transformation a Householder reflection is 2-norm preserving.
Thus a Housholder reflection can only reflect unit vectors x "to be
[the] jth column of [the] identity". Householder reflections are meant
to apply to any nonzero vector x, not just unit vectors. A correct
description might read "to be [a] multiple of [the] jth column of [the]
identity".


Regards,

Vic

-- 
*---* mailto:vic at norton dot name
|     Victor Thane Norton, Jr.
|     Mathematician and Motorcyclist
|     phone: 419-353-3399
*---* http://vic.norton.name



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