I need some clarification on projections of complex vectors. If I have a nxm matrix of complex numbers V and a mx1 matrix s, and I want to find the projection of s onto any column of V. The formula to do this is c = <V, s>/||V(j)||^2 where V(j) is the column of V to be used. My question is, what is <V,s>? is that the inner product of the whole matrix V with s, or is it the inner product of V(j) with s? Where V or V(j) would be the Hermition of the vector.