The vectorization of a $m\!\times\!n$ matrix $A = (a_{ij})$ transforms the matrix to a column vector $\mbox{vec}(A)$ , which consists of all columns of $A$ stacked in sequence: $$\mbox{vec}(A) \;:=\; \left(a_{11}\;\;a_{21}\;\ldots\;a_{m1}\;\;\;a_{12}\;\;a_{22}\;\ldots\;a_{m2}\;\; \ldots\;\ldots\;\;a_{1n}\;\;a_{2n}\;\ldots\;a_{mn}\right)^\intercal$$ The mapping vec from the vector space formed by the $m\!\times\!n$ matrices to the vector space of the column vectors of the length $mn$ is apparently a linear transformation.