Gram-Schmidt Orthonormalization: Modifying Vectors & Spanning Space

[dntmn]

I have a question about Gram Schmidt Orthonormalization. I know you can orthogonalize then normalize.

My question is can you (multipy/divide) the given vectors by a scalar to give new vectors, then orthogonalize(by taking projection), then normalize the result?

would the result still span the space of the orgional vectors?

 

[StatusX]

Of course, just imagine the scalar hanging out front the whole time, then it goes away when you normalize at the end.

 

[dntmn]

Thank you!