v.v = ||v|?.V.V = For any scalar c, u- (cv) = c(u v). If the distance from u to v equals the distance from u to-v, then u and v

are orthogonal. For a square matrix A, vectors in Col A are orthogonal to vectors in Nul A. If vectors v1,...,V, span a subspace W and if x sorthogonal to each v, for j = 1,.... p, then x is in w1