Can Each Vector Be Made Orthonormal Directly in Gram-Schmidt Process?

[gbartel]

I have a question regarding the Gram-Schmidt process. When solving for the new subspace, is it okay to make a newly calculated vector orthonormal before calculating the rest of the vectors? I've always first solved for the vectors then made all the calculated vectors orthonormal, but I'd like to make each vector orthonormal directly after each one is calculated. I figured this might corrupt the vectors beyond the first one.

Thanks in advance!

 

[gerben]

Yes, that is okay. You can first orthogonalize all and then normalize all, or immediately normalize after you have orthogonalized, or normalize some in between the orthogonalization, whatever you want, the order does not matter.

 

[gbartel]

Awesome thanks!