Definition:Vectorization of Matrix/Definition 2

Definition
Let $S$ be a set.

Let $m, n \ge 1$ be natural numbers.

Let $A = \sqbrk {a_{i j} }$ be a $m \times n$ matrix over $S$.

Let $R$ be a ring with unity.

Let $A$ be an $m \times n$ matrix over $R$.

The vectorization of $A$ is its coordinate vector with respect to the standard matrix basis.

Also see

 * Equivalence of Definitions of Vectorization of Matrix