I've seen a few times the notation ${}_{\mathcal B}[h]_{\mathcal A}$ for the matrix of a linear map $h\colon E\to F$ with respect to a base $\mathcal A$ of $E$ and a base $\mathcal B$ of $F$. I imagine that the notation for the column of coordinates of an element $v$ of $E$ in the base $\mathcal A$ is then ${}_{\mathcal A}[v]$.
This notation is quite practical indeed: $$ {}_{\mathcal B}[h(v)] = {}_{\mathcal B}[h]_{\mathcal A}{}_{\mathcal A}[v],\quad {}_{\mathcal C}[kh]_{\mathcal A} = {}_{\mathcal C}[k]_{\mathcal B}{}_{\mathcal B}[h]_{\mathcal A}. $$
I've though also of a possible alternative notation inspired by Ricci calculus conventions: $[h]_{\mathcal A}^{\mathcal B}$ could denote the matrix of $h\colon E\to F$ and $[v]^{\mathcal A}$ could denote the column of coordinates of $v\in E$, and then $$ [h(v)]^{\mathcal B} = [h]_{\mathcal A}^{\mathcal B}[v]^{\mathcal A},\quad [kh]_{\mathcal A}^{\mathcal C} = [k]_{\mathcal B}^{\mathcal C}[h]_{\mathcal A}^{\mathcal B}. $$
Is there some reputable textbook on linear algebra or a related topic that uses some such notation?
Relevant observations
Serge Lang in his Linear Algebra used the notation $M^{\mathcal A}_{\mathcal B}(h)$ for the matrix of $h$ and $X_{\mathcal A}(v)$ for the column of coordinates of $v$, thus making the opposite choice of lower and upper indices to what I suggest. The use of upper and lower indices in matrices in his book is also opposite to that of Ricci calculus.