
316 High Performance Programming for Soft Computing
3. The orthogonal vector should be normalized,
(15.3.24)
4. In the j
th
step, the vector (15.3.25) is found,
(15.3.25)
Therefore, the Gram-Schmidt process allows us to construct the
orthonormal set which spans a k-dimensional subspace
in
.
For arbitrary , and , the linear operator A provides a
map if (15.3.26) is satisfi ed.
121 2
(| |) | | ,Acxc cAxcAy+= +
(15.3.26)
For the orthonormal basis and the arbitrary vector in ,
where , using the linear operator implies that,
(15.3.27)
The Hermitian conjugate of the linear operator for the
arbitrary vectors
, is defi ned