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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.
1 Uniqueness of elimination matrix. 1 comment. Toggle the table of contents. Talk: Duplication and elimination matrices.
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.
The problem with the Gauss–Jordan elimination article is that it says Gaussian elimination does not bring a matrix to reduced row echelon form, but the Gaussian elimination article says it does. Jitse Niesen says that Gaussian elimination does not bring a matrix to reduced row echelon form, but did not comment further on the contradiction ...
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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 ...