Orthogonalize, Normalize, and Projection have been added to the built-in Mathematica kernel. Normalize can now take an arbitrary norm function.
Orthogonalize gives an orthonormal basis found by orthogonalizing the vectors:
Orthogonalize can generate an orthonormal basis for the vectors with respect to an inner product function which is the second argument of the function:
Use an arbitrary norm function:
Version 5.2 returns unevaluated
This finds the projection of a vector onto another vector assuming x, y, a, b are Real:
Householder was available in previous versions of Mathematica and is now available on the web at library.wolfram.com/infocenter/MathSource/6829.