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.)
The Haar basis is the basis of the row vectors, not of the column vectors, so I presume you'd want to solve the equation $zH=x$ for row vectors instead. That also makes sense in that $x$ and $y$ are being specified as row vectors.