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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.
During execution of the Bareiss algorithm, every integer that is computed is the determinant of a submatrix of the input matrix. This allows, using the Hadamard inequality, to bound the size of these integers. Otherwise, the Bareiss algorithm may be viewed as a variant of Gaussian elimination and needs roughly the same number of arithmetic ...
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 ...
The individual entries have a copy-on-write behavior that is non-aliasing, i.e. changing one copy afterwards will not affect other copies. [9] Microsoft's ReFS also supports this operation. [10] Target deduplication is the process of removing duplicates when the data was not generated at that location.
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.
Kron reduction is a useful tool to eliminate unused nodes in a Y-parameter matrix. [2] [3] For example, three linear elements linked in series with a port at each end may be easily modeled as a 4X4 nodal admittance matrix of Y-parameters, but only the two port nodes normally need to be considered for modeling and simulation.
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One other popular approach is the Recursive Feature Elimination algorithm, [15] commonly used with Support Vector Machines to repeatedly construct a model and remove features with low weights. Embedded methods are a catch-all group of techniques which perform feature selection as part of the model construction process.