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 represents the -th element of matrix and the superscript denotes the transpose. Vectorization expresses the isomorphism  between these vector spaces (of matrices and vectors) in coordinates.