I am wondering if there is a special name for an $m\times n$ matrix $A=(a_{i,j})$, with $a_{i,j}\in\{0,1\}$ that will pick $m$ unique components from a vector $v\in\mathbb{R}^n$ ($m\le n$), it is similar to a projection matrix, except that the image of such matrix is the subspace $\mathbb{R}^m$ instead of $\mathbb{R}^n$. Is decimation matrix correct?
For example, given a vector $v=(v_i)_{1\le i\le n}\in\mathbb{R}^n$, such matrix may return $w=(v_i)_{i=1,3,\ldots,2\lfloor \frac{n-1}{2}\rfloor+1}$ or $(v_i)_{1\le i\le 4}$ or any subset of the vector components.
Closely related question (without the coordinate position advancing requirement): Matrix with exactly one 1 in each row