Vectorization (Mathematics): Mathematics, Linear Algebra, Matrix Theory, Linear Transformation, Matrix (Mathematics) - Brossura

 
9786131136979: Vectorization (Mathematics): Mathematics, Linear Algebra, Matrix Theory, Linear Transformation, Matrix (Mathematics)

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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. For a symmetric matrix A, the vector vec(A) contains more information than is strictly necessary, since the matrix is completely determined by the symmetry together with the lower triangular portion, that is, the n(n+1)/2 entries on and below the main diagonal. For such matrices, the half-vectorization is sometimes more useful than the vectorization. There exist unique matrices transforming the half-vectorization of a matrix to its vectorization and vice-versa called, respectively, the duplication matrix and the elimination matrix.

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