Definition:Vectorization of Matrix/Definition 2
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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.