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Subject: Re: orthonormalizing l.d. vectors

giff wrote:
> Hi all,
> my skills in geometry and linear algebra are not so good, so I apologize
> if my question sounds stupid or inappropriate.
> I have got N vector of lenght V, they are not linearly independent. I
> need to make these vectors orthonormal.

Decomposition in an orthonormal base ?

> I don't really know how to do this, since the vectors are not lin. ind.
> (in that case I would apply Gram-Schmidt).

Why not?

q1 ... qn orthonormal base

Q = V1
m = Q dot Q
c11 = sqrt(m)
q1 = Q/c11

c21 = V2 dot q1
Q = V2 - c21*q1
m = Q dot Q
c22 = sqrt(m)
q2 = Q/c22

c31 = V3 dot q1
c32 = V3 dot q2
Q = V3 - c31*q1 - c32*q2
m = Q dot Q
c33 = sqrt(m)
q3 = Q/c33


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