Orthogonalization of a basis

Questions
1

Hi,
The function Orthogonalize basically applies Gram Schmidt orthonormalization.
Is there a way to orthogonalize without normalizing the vectors?
Thank you.

2

There is an answer to similar question here orthogonalizing-without-normalizing that might be of help.

3

Thank you, but I have already tried it and unfortunately it does not work.

I used OrthogonalMatrixQ to verify whether it comes out orthogonal and it does not.