[SOLVED] Vectors that form bases (linear algebra) 1. The problem statement, all variables and given/known data I am given two vectors u and v, which are: u = (1/2 , 1/2 , 1/2 , 1/2) and v = (1/2 , 1/2 , -1/2 , -1/2). I have to find an orthonormal basis for R^4 containing u and v. 3. The attempt at a solution The first thing that came to me was Gram-Schmidt - but then I saw that the dot-product between u and v is zero, so Gram-Schmidt is overkill. I just need to find two other linearly independant vectors that has dot-product equal zero with respectively u and v. Is that even possible and how would I do that?