Orthogonalization is the construction, from a linearly independent list 
,
,
..., 
in an inner product space, of an orthogonal
set 
,
,
..., 
having the same successive spans,
 |
for every 
from 1 through 
.
Dividing each 
by its norm gives an orthonormal list. The standard construction
is the Gram-Schmidt orthonormalization;
numerically, Householder matrices and Givens
rotations are often used to obtain a QR decomposition
more stably.
