Vectorization (mathematics)
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.
For example, for the 2×2 matrix =, the vectorization is .
Read more about Vectorization (mathematics): Compatibility With Kronecker Products, Compatibility With Hadamard Products, Compatibility With Inner Products, Half-vectorization, Programming Language