Vec Function

Definition

Let

• $A$ : $n\times m$ matrix
• $c_1,\dots ,c_m$ : Column vectors of $A$

Then Vec function is defined as

$$\mathrm{vec}(A)=\left[\begin{array}{c}{c}_1\\ ⋮\\ c_m\end{array}\right]$$

Example

Let $A=\left[\begin{array}{ccc}1& 3& 5\\ 2& 4& 6\end{array}\right]$

Then $c_1=\left[\begin{array}{c}1\\ 2\end{array}\right]$, $c_2=\left[\begin{array}{c}3\\ 4\end{array}\right]$, $c_3=\left[\begin{array}{c}5\\ 6\end{array}\right]$

$$\mathrm{vec}(A)=\left[\begin{array}{c}{c}_1\\ c_2\\ c_3\end{array}\right]=\left[\begin{array}{c}1\\ 2\\ 3\\ 4\\ 5\\ 6\end{array}\right]$$