I've learned the process of orthogonal diagonalisation in an algebra course I'm taking...but I just realised I have no idea what the point of it is.
The definition is basically this: "A matrix A is orthogonally diagonalisable if there exists a matrix P which is orthogonal and D = PtAP where D is diagonal". I don't understand the significance of this though...what is special/important about this relationship?