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.
