I cannot visualise an oblique projection. I understood the orthogonal one: The orthogonal projection is P=U[tex]\cdot[/tex]U*, where U is an orthonormal matrix (basis of a subspace) : U*[tex]\cdot[/tex]U=I . Now the projection of matrix A on U vectors is: PA=U*[tex]\cdot[/tex]A[tex]\cdot[/tex]U . For the orthogonal projection, for a vector case, the geometry is simple: you project a vector x on the direction of a vector v, and the projected vector is the one from the origin to the base of the perpendicular from x on the direction v: vv*x = vk, where k is the length of the projection (the coordinate of x in v direction), k=v*x = |v|*|x|*cos(v,x)= x*cos (where |v|=1). Now an oblique projection is defined as: OP=WV* , where V*W=I. So the oblique projection of A is OPA=V*AW. Can you please explain what an oblique projection is? Geometrically I mean. For a vector case first. I'm guessing the projection of vector x should be the vector in the direction of w but up to the point where the direction of v through x intersects the direction of w. But v*w = I. I cannot see this in a plane . Not to mention the projection of a matrix (the column vectors of it I guess). A drawing would be nice :D.