Square Brackets With Superscript & Subscript on Vector Space Does anybody know what the following notation means?
(I'm referring to the subscript & superscript to the right of the square brackets)
$\psi(T)=[T]_β^γ$
In this case, $T: V \rightarrow W$ is a linear map on finite-dimensional vector spaces $V$ & $W$ (over the same field $F$) with dimensions $n$ and $m$ resp. And, $\beta$ & $\gamma$ are ordered bases for resp. $V$ & $W$. Lastly, $\psi$ is the isomorphism $\psi:L(V,W)→M_{m\times n}(F)$.
(Full context here Proving isomorphism between linear maps and matrices)

The expression on the right represents the matrix of the operator $T:V\to W$ with respect to the bases $\beta$ of $V$ and $\gamma$ of $W$.
More specifically, one evaluates T at the $j$-th basis vector in $\beta$ and expresses the output as a linear combination of basis vectors from $\gamma$. The respective coefficients in the linear combination form the $j$-th column of the matrix $[T]_{\beta}^{\gamma}$.
