# vectorization of matrix

The vectorization of a $m\!\times\!n$ matrix  $A=(a_{ij})$  the matrix to a column vector $\mbox{vec}(A)$, which consists of all columns of $A$ stacked in :

 $\mbox{vec}(A)\;:=\;\left(a_{11}\;\;a_{21}\;\ldots\;a_{m1}\;\;\;a_{12}\;\;a_{22% }\;\ldots\;a_{m2}\;\;\ldots\;\ldots\;\;a_{1n}\;\;a_{2n}\;\ldots\;a_{mn}\right)% ^{\intercal}$

The mapping vec from the vector space formed by the $m\!\times\!n$ matrices to the vector space of the column vectors of the $mn$ is apparently a linear transformation.

Title vectorization of matrix VectorizationOfMatrix 2013-03-22 18:12:20 2013-03-22 18:12:20 pahio (2872) pahio (2872) 4 pahio (2872) Definition msc 15-01 vectorization vectorisation transpose