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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.
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.
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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If Gaussian elimination applied to a square matrix A produces a row echelon matrix B, let d be the product of the scalars by which the determinant has been multiplied, using the above rules. Then the determinant of A is the quotient by d of the product of the elements of the diagonal of B : det ( A ) = ∏ diag ( B ) d . {\displaystyle \det ...
On the morning of Dec. 26, 1996, John and Patsy Ramsey woke up to find their 6-year-old daughter, JonBenét Ramsey, missing from her bedroom. Shortly after, they found a handwritten ransom note ...