What is "vectorization"

alt. the action of vectorizing n. the action of vectorizing

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:

vec(A) = [a, …, a, a, …, a, …, a, …, a]
Here a represents the (i, j)-th element of matrix A and the superscript denotes the transpose. Vectorization expresses the isomorphism R :  = R ⊗ R ≅ R between these vector spaces (of matrices and vectors) in coordinates.

For example, for the 2×2 matrix A = $\begin{bmatrix} a & b \\ c & d \end{bmatrix}$, the vectorization is $\mathrm{vec}(A) = \begin{bmatrix} a \\ c \\ b \\ d \end{bmatrix}$.

Vectorization may refer to:

• Vectorization (mathematics), a linear transformation which converts a matrix into a column vector.
• Array programming, a style of computer programming where operations are applied to whole arrays instead of individual elements.
• Automatic vectorization, a compiler optimization that transforms loops to vector operations.
• Vectorization (image tracing), is the creation of vector from raster graphics.
• Drug vectorization, to (intra)cellular targeting.