Solving Orthonormal System with Gram-Schmidt

[Niles]

[SOLVED] Orthonormal system

Homework Statement

I have three vectors, u_1, u_2 and u_3, in R^4. I want to find an orthonormal system v_1, v_2 and v_3, where:

span(u_1, u_2, u_3) = span(v_1, v_2, v_3).

The Attempt at a Solution

My "guess" is that I can just use Gram-Schmidt on u_1, u_2 and u_3 to find the orthonormal system, and the two vector-sets must span the same space, right?

Thanks in advance,

sincerely Niles.

 

[quantumdude]

Yes, you are supposed to use Gram-Schmidt.