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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.
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"
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President-elect Donald Trump campaigned relentlessly on grocery prices in the 2024 race, vowing to bring down costs quickly for American families if given four more years in the White House.
The ACH matrix can be problematic when analyzing a complex project. It can be cumbersome for an analyst to manage a large database with multiple pieces of evidence. Evidence also presents a problem if it is unreliable. The evidence used in the matrix is static and therefore it can be a snapshot in time.