I want to help one of my friends who studies engineering. He has a homework at the signal processing course. I think I realize what I have to do, but since I don't have their course, I do not fully understand what I have to do. It goes like this:
$ H=\begin{pmatrix}1&-1&0&0&0&0&0&0 \\ 0&0&1&-1&0&0&0&0 \\ 0&0&0&0&1&-1&0&0\\ 0&0&0&0&0&0&1&-1 \\ 1&1&-1&-1&0&0&0&0\\ 0&0&0&0&1&1&-1&-1 \\ 1&1&1&1&-1&-1&-1&-1\\ 1&1&1&1&1&1&1&1 \end{pmatrix}$
The exercise says to check that $H$ consists of independent line vectors (that's easy). Then it says to find the coordinates of $x=[1,1,...1]$ and $y=[1,-1,...,1,-1]$ in the Haar Basis defined by $H$.
Does this means to find the coordinates in the usual way, i.e. solve the equation $zH=x$?
(I do not need you to solve the system (I'll use Matlab for that), just say if I'm right or not. Thank you.)