If one wants to use matrices in such way that one does "per dimension" transformations (e.g. if the dimensions are $x_1, ..., x_n$, then one would like to do $f_1(x_1), ..., f_n(x_n)$), then is the matrix suitable?
That is, because when one uses matrices for e.g. multiplication, the element $a_{ij}$ in the result $AB$ is the dot product between row $i$ in $A$ by row $j$ in $B$.
But doesn't this mean that one applies "other dimensional" modifications to the original elements? That is, $a_{11}$ may be in "first dimension" (whatever one uses it for), but in the matrix multiplication all the effects of the other $n-1$ dimensions are also summed to this, because one sums over the entire row and column, rather than just performs the operation on that single element. So the resulting $a_{11}$ reflects not only "modifications" done in the first dimension, but all the $n-1$ other as well.
So if using matrix transformations for "per dimension processing", how is the matrix used?