**comp.graphics.algorithms**

## 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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