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Vec Des Sonagrammes De Flûtes à Bec
Vec may mean: Mathematics: * vec(''A''), the Vectorization_(mathematics), vectorization of a matrix ''A''. * Vec denotes the category of vector spaces over the reals. Other: * Venetian language (Vèneto), language code. * Vecuronium, a muscle relaxant. * vec, a sentient moravec robot from the Orion's Arm Universe Project (see also Moravec_(robot)) See also * VEC (other) {{Disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 vector. Specifically, the vectorization of a matrix ''A'', denoted vec(''A''), is the column vector obtained by stacking the columns of the matrix ''A'' on top of one another: \operatorname(A) = _, \ldots, a_, a_, \ldots, a_, \ldots, a_, \ldots, a_\mathrm Here, a_ represents the element in the ''i''-th row and ''j''-th column of ''A'', and the superscript ^\mathrm denotes the transpose. Vectorization expresses, through coordinates, the isomorphism \mathbf^ := \mathbf^m \otimes \mathbf^n \cong \mathbf^ between these (i.e., of matrices and vectors) as vector spaces. For example, for the 2×2 matrix A = \begin a & b \\ c & d \end, the vectorization is \operatorname(A) = \begin a \\ c \\ b \\ d \end. The connection between the vectorization of ''A'' and the vectorization of its transpose is given by the commutation matrix ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |