Let $v_1,...,v_n\in\Bbb R^d$ be a sequence of vectors. When we say that we "linearly transform" this sequence, we mean that we apply a linear transformation $T\in\Bbb R^{d\times d}$ to each vector in the sequence individually. 
This can also be expressed as applying the transformations $T$ from the *left* to the following matrix, and then reading off the columns of the resulting matrix:

$$
\newcommand{\verts}{\rule{0.2pt}{1.3em}}
\Phi(\boldsymbol v):=\begin{bmatrix}
    \verts & \!\verts & & \verts \\[-1ex]
\,v_1 & \!v_2 & \!\!\!\cdots\!\!\! & v_n\, \\
    \verts & \!\verts & & \verts
\end{bmatrix}\in\Bbb R^{d\times n}
$$

> **Question:** Is there an established name for what I am doing when I apply a linear transformation $S\in\Bbb R^{n\times n}$ from the *right* to this matrix and then read off the columns?
>
>$$v_1,...,v_n \,\overset S\mapsto\, w_1,...,w_n,\quad \text{if}\,\; \Phi(\boldsymbol w)=\Phi(\boldsymbol v)S.$$

<!--$$
\newcommand{\horz}{\rule[0.4ex]{1.3em}{0.2pt}}
\Phi(\boldsymbol v):=\begin{bmatrix}
    \;\,\horz\!\!\! & v_1 & \!\!\!\horz\;\, \\
    \;\,\horz\!\!\! & v_2 & \!\!\!\horz\;\, \\
    & \vdots &  \\
    \;\,\horz\!\!\! & v_n & \!\!\!\horz\;\,
\end{bmatrix}\in\Bbb R^{n\times d}
$$-->

Examples of this are:
 * permuting the vectors in the sequence ($S$ is a permutation matrix).
 * scaling each vector individually ($S$ is a diagonal matrix). 

Neither of this falls under "linearly transforming the sequence" with the usual meaning. But it is still linear in some sense, and I would like to have a suitable terminology to refer to these transformations.


I suppose these sort of transformations can be called *column operations* on $\Phi(\boldsymbol v)$, but I wonder specifically whether there is a name for the operations when we think of vector sequences and want to avoid thinking of matrices and explicit basis representations. I am mostly interested in the case when $S$ is invertible.