Matrix Vectorization

1. Vectorization of any \(M \times N\) Matrix \(A\) involves taking each Column of Elements of Matrix \(A\) and placing them one below the other in a Single Column, thereby making a \(MN \times 1\) Column Matrix/Vector as given below
   
   \(A=\begin{bmatrix} a_{11} & a_{12} & ... & a_{1n}\\ a_{21} & a_{22} & ... & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\a_{m1} & a_{m2} & ... & a_{mn}\end{bmatrix}\hspace{.6cm} \Rightarrow Vec\hspace{.1cm}(A)= \begin{bmatrix} a_{11} \\ a_{21} \\ \vdots \\ a_{m1} \\ a_{12} \\ a_{22} \\ \vdots \\ a_{m2} \\ \vdots \\ a_{1n} \\ a_{2n} \\ \vdots \\ a_{mn}\end{bmatrix}\)