I am following "Sparse and redundant representations - from theory to application in image and signal processing" by Michael Elad.
Let $A\in \mathbb R^{m\times n}$ and $m>n$.
On the beginning of the third chapter:
"Looking at the problem ($P_0$):
$$P_0: \min_{x} \|x\|_0 \text{ subject to } Ax=b$$
one observes that the unknown $x$ is composed of two effective parts to be found – the support of the solution, and the non-zero values over this support."
I cannot find the meaning behind "the support of the solution".
If I understand correctly, as we are looking at the $\ell_0-norm$, we are trying to find the vector $x$ containing a minimum number of non-zeroes which answers $Ax=b$. In other words, A linear combination of some of the columns in $A$. Is it correct to say that the support is the set of columns in $A$ used for the linear combination?