Let vec(X) denote the "vectorize" operation that returns as its output a vector in FMN formed by stacking the N columns of X FMN on top of each other. For vectors x FM and y FN, so that xyT FMN, prove that vec(xyT)=yx FMN. Verify (for yourself) by using commands vec(x * y') and kron(y, x) in Julia for some real vectors, and using vec(x * transpose(y)) for some complex vectors. (The equality above does not hold for vec(xy) when y is complex.)