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In mathematics, especially in linear algebra and matrix theory, the duplication matrix and the elimination matrix are linear transformations used for transforming half-vectorizations of matrices into vectorizations or (respectively) vice versa.
In chemical analysis, matrix refers to the components of a sample other than the analyte [1] of interest. The matrix can have a considerable effect on the way the analysis is conducted and the quality of the results are obtained; such effects are called matrix effects. [ 2 ]
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.
Row echelon form — a matrix in this form is the result of applying the forward elimination procedure to a matrix (as used in Gaussian elimination). Wronskian — the determinant of a matrix of functions and their derivatives such that row n is the (n−1) th derivative of row one.
Duplication, or doubling, multiplication by 2; Duplication matrix, a linear transformation dealing with half-vectorization; Doubling the cube, a problem in geometry also known as duplication of the cube; A type of multiplication theorem called the Legendre duplication formula or simply "duplication formula"
Research suggests that less than six hours of sleep is associated with an increased risk of cognitive impairment and high blood pressure. ... One of the study’s strengths was its large sample ...
A decades-old cosmetic procedure called mesotherapy, which involves injecting unregulated mixtures of vitamins and drugs under the skin to reduce under-eye bags, is regaining popularity in the US.
4. Use a Long Tug Toy. A long tug toy may also come in handy, as it encourages the puppy to play with us without involving our bodies. A long tug toy works best because it creates distance between ...