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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 a m × n matrix A, denoted vec(A), is the mn × 1 column vector obtained by stacking the columns of the matrix A on top of one another: Here, represents and the superscript denotes the transpose. Vectorization expresses, through coordinates, the isomorphism between these (i.e., of matrices and vectors) as vector spaces. For example, for the 2×2 matrix , the vectorization is .