**comp.graphics.algorithms**

## Subject: **Re: orthonormalizing l.d. vectors**

In article

says...

> 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.

>

> I don't really know how to do this, since the vectors are not lin. ind.

> (in that case I would apply Gram-Schmidt).

The problem divides into two:

1) Pick a maximal linearly independent set of vectors T from V

2) Use Gram-Schmidt on T

You know how to do 2), here is 1)

Place your vectors V in a matrix A as rows vectors. Convert the matrix

into the Row-Reduced Echelon Form (RREF) using elementary row

operations. Call this matrix R.

The non-zero row vectors in R form a basis for the subspace spanned by

V. Their count is r = rank(A) = rank(R), since the row-operations do not

change the rank.

If you wish to select r vectors from the original set V, map the non-

zero vectors from R using the inverse of the matrix which transformed A

to the RREF form. Select the non-zero vectors and you are done.

--

Kalle Rutanen

http://kaba.hilvi.org

Reply

View All Messages in

**comp.graphics.algorithms**

path:

orthonormalizing l.d. vectors =>

Replies:

Copyright © 2006 WatermarkFactory.com. All Rights Reserved.