1: Orthogonal Matrices Let R be an nn matrix, and let ri Rn be the i-th column of R. R is said to be orthogonal, if for any i= j, the vectors ri and rj are orthogonal to each other, and each ri is unit length. For this class, we then also say that the vectors {r1,...,rn} form an orthonormal basis for Rn if the determinant is 1 (following the right-hand rule)