4 ms·
nit: the identity matrix is a projection P^2 = P is the definition. not losing dimensions
by nh23423fefe 3y ago
nit: the identity matrix is a projection
P^2 = P is the definition. not losing dimensions
- amelius 3y agoTrue, but missing the point as you would not normally refer to the identity matrix as a projection.
- nh23423fefe 3y agoWhat was your point? An incorrect characterization of projections?
- mrfox321 3y agoNit to your nit, which is incorrect w.r.t. parent reply: A Fourier transform is not a projection, it's a change of basis represented by a unitary transformation.
- ndriscoll 3y agoThe w Fourier coefficient F(w) is the dot product of f with an exponential function, `e_w • f`, and is in that sense a projection. The inverse Fourier transform writes the original function as a sum of the projected components: `f = sum_w (e_w • f) e_w = sum_w F(w) e_w`. This is exactly how writing an "arrow" style 2- or 3-D vector as a sum of orthogonal projections works.