I'm reading a book which uses some linear algebra, and the author states an equality of the form $C \ vec(A) = c$, where $C$ is said to be a selection matrix. What's a selection matrix? I've searched the internet, but I only get results for a kind of decision helping matrix used in business management…
Any help would be appreciated.
Best Answer
Left-multiplying a matrix $M$ by the $i$th row of the identity matrix picks out the $i$th row of $M$; right-multiplying by the $j$th column of the identity picks out the $j$th column of $M$. I would guess that $C$ consists of the appropriate rows of the identity to select the desired elements of $\operatorname{vec}(A)$. For example, if $\operatorname{vec}(A)$ has five elements and you want to end up with a vector that consists of the second and fourth elements, you would use $$C = \begin{bmatrix}0&1&0&0&0\\0&0&0&1&0\end{bmatrix}.$$