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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.
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 ...
A home invasion in an upscale Philadelphia suburb turned fatal over the weekend after a suspect broke into a home in Lower Merion Township at 2:20 a.m. on Sunday, Dec. 8, the Montgomery County ...
10 Genius Things Warren Buffett Says To Do With Your Money. This article originally appeared on GOBankingRates.com: 5 Economic Changes That Could Be Coming When Trump Takes Office in January.
Gaussian elimination is the main algorithm for transforming every matrix into a matrix in row echelon form. A variant, sometimes called Gauss–Jordan elimination produces a reduced row echelon form. Both consist of a finite sequence of elementary row operations; the number of required elementary row operations is at most mn for an m-by-n ...
The woman, who identified herself as Shay, told The Post she saw the truck on Tuesday and her surveillance footage shows the vehicle's lights turn on at around 12:25 a.m. on New Year's Day.