Let $\mathbf{A}=\begin{bmatrix} A_{11} & A_{12} & \cdots & A_{1m} \\ A_{21} & A_{22} & \cdots & A_{2m} \\ \vdots & \vdots & \cdots & \vdots \\ A_{m1} & A_{m2} & \cdots & A_{mm} \end{bmatrix}$ be a block matrix where each $A_{ij}$, $1\leq i,j\leq m$, is an

$n\times n$ matrix. Define operator $VB$ by

$VB(\mathbf{A})=\begin{bmatrix} A_{11} \\ A_{21} \\ \vdots \\ A_{m1} \\ A_{12} \\ \vdots \\ A_{mm} \end{bmatrix}$

What is called operator $VB$? Is there any reference about its properties?