In
mathematics, especially in
linear algebra and
matrix theory, the
vectorization of a
matrix is a
linear transformation which converts the matrix into a
column vector. Specifically, the vectorization of an
m×n matrix
A, denoted by vec(
A), is the
mn × 1 column vector obtained by stacking the columns of the matrix
A on top of one another:
Here
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=2894)
represents the
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=3711)
-th element of matrix
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=1980)
and the superscript
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=2800)
denotes the
transpose. Vectorization expresses the
isomorphism ![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=3539)
between these vector spaces (of matrices and vectors) in coordinates.