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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.
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.
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.
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"
In linear systems, indeterminacy occurs if and only if the number of independent equations (the rank of the augmented matrix of the system) is less than the number of unknowns and is the same as the rank of the coefficient matrix. For if there are at least as many independent equations as unknowns, that will eliminate any stretches of overlap ...
A top Costco executive sounded the alarm on the potential consequences of President-elect Donald Trump’s proposed tariffs — warning that it will raise prices of goods across the board. “When ...
The Crout matrix decomposition algorithm differs slightly from the Doolittle method. Doolittle's method returns a unit lower triangular matrix and an upper triangular matrix, while the Crout method returns a lower triangular matrix and a unit upper triangular matrix. So, if a matrix decomposition of a matrix A is such that: A = LDU
Macy’s would be more valuable if it just shut down its business and sold everything off for parts. That’s the argument activist investment firm Barington Capital and private equity firm Thor ...