Search results
Results from the WOW.Com Content Network
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 example, for the 2×2 matrix = [], the half-vectorization is = []. There exist unique matrices transforming the half-vectorization of a matrix to its vectorization and vice versa called, respectively, the duplication matrix and the elimination matrix .
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 ...
For example, we might swap rows to perform partial pivoting, or we might do it to set the pivot element , on the main diagonal to a non-zero number so that we can complete the Gaussian elimination. For our matrix (), we want to set every element below , to zero (where , is the element in the n-th column of 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.
Trump will probably make a show of eviscerating Biden’s climate plans while rebranding some of them as his own. Markets, in the end, may move in more or less the same direction.
Two years ago, she graduated with her Ph.D. in biomedical sciences. She now works in the research lab at the University of Minnesota, studying how genetic modifications can help people heal. She ...
In mathematics, the Bruhat decomposition (introduced by François Bruhat for classical groups and by Claude Chevalley in general) = of certain algebraic groups = into cells can be regarded as a general expression of the principle of Gauss–Jordan elimination, which generically writes a matrix as a product of an upper triangular and lower triangular matrices—but with exceptional cases.