Hi Ning,
Not exactly. If you want to convince yourself that it is not right,
imagine a case where A=B=C,
then your method will give:
Aorth=A - A(A.A)/(A.A) - A(A.A)/(A.A) = -A
While the true answer is 0.
You need to use the Gram-Schmidt orthogonalisation process:
A1 = A - B.(A.B)/(B.B)
A2 = A1 - C.(A1.C)/(C.C)
etc. (here Aorth=A2)
Which gives 0 if A=B=C !
Cheers,
Saad.
On 16 Jan 2009, at 04:45, Ning Liu wrote:
> Hi,
>
> I know
>
> To orthogonalise vector A wrt B:
>
> Aorth = A - B (A.B)/(B.B)
>
>
> But how we do orthogonalise vector A wrt B, C, D ...
>
> is it like
>
> Aorth = A- B (A.B)/(B.B) - C (A.C)/(C.C)-...
>
> ?
>
>
> Thanks,
>
>
> Ning
>
Saad Jbabdi
Oxford University FMRIB Centre
JR Hospital, Headington, OX3 9DU, UK
+44 (0) 1865 222545 (fax 717)
www.fmrib.ox.ac.uk/~saad
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