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vectori
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There are 7 letters in VECTORI ( C3E1I1O1R1T1V4 )
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VECTORI - In mathematics, especially in linear algebra and matrix theory, the vectorization of a matrix is a linear transformation which converts the matrix in...
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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 an 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:* * * * * v * e * c * * ( * A * ) * = * [ * * a * * 1 * , * 1 * * * , * … * , * * a * * m * , * 1 * * * , * * a * * 1 * , * 2 * * * , * … * , * * a * * m * , * 2 * * * , * … * , * * a * * 1 * , * n * * * , * … * , * * a * * m * , * n * * * * ] * * * T * * * * * * {\displaystyle \mathrm {vec} (A)=[a_{1,1},\ldots ,a_{m,1},a_{1,2},\ldots ,a_{m,2},\ldots ,a_{1,n},\ldots ,a_{m,n}]^{\mathrm {T} }} * Here, * * * * * a * * i * , * j * * * * * {\displaystyle a_{i,j}} * represents * * * * A * ( * i * , * j * ) * * * {\displaystyle A(i,j)} * and the superscript * * * * * * * * * * T * * * * * * {\displaystyle {}^{\mathrm {T} }} * denotes the transpose. Vectorization expresses, through coordinates, the isomorphism * * * * * * R * * * m * × * n * * * := * * * R * * * m * * * ⊗ * * * R * * * n * * * ≅ * * * R * * * m * n * * * * * {\displaystyle \mathbf {R} ^{m\times n}:=\mathbf {R} ^{m}\otimes \mathbf {R} ^{n}\cong \mathbf {R} ^{mn}} * between these (i.e., of matrices and vectors) as vector spaces. * For example, for the 2×2 matrix * * * * A * * * {\displaystyle A} * = * * * * * * [ * * * * a * * * b * * * * * c * * ... |