1. The problem statement, all variables and given/known data Prove: if an n × n matrix A is orthogonal (column vectors are orthonormal), then the columns form an orthonormal basis for R^n. (with respect to the standard Euclidean inner product [= the dot product]). 2. Relevant equations None. 3. The attempt at a solution I know that since the column vectors are orthonormal, all I have to show is that these vectors are also linearly independent and span R^n. But I'm having some trouble showing this, so I was thinking about showing it through the basis coordinates: u= <u, v1>v1 + <u, v2>v2 +...+ <u, vn>vn But I think I have to start with assuming that the vectors v1, v2, ... vn form a basis. So I think that method can't work.