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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.
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 ...
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 ...
These decompositions summarize the process of Gaussian elimination in matrix form. Matrix P represents any row interchanges carried out in the process of Gaussian elimination. If Gaussian elimination produces the row echelon form without requiring any row interchanges, then P = I, so an LU decomposition exists.
(Reuters) -U.S. President-elect Donald Trump's transition team is exploring ways to significantly reduce, merge, or even eliminate the top bank regulators in Washington, the Wall Street Journal ...
The purpose of this step is to identify, validate and select a root cause for elimination. A large number of potential root causes (process inputs, X) of the project problem are identified via root cause analysis (for example, a fishbone diagram). The top three to four potential root causes are selected using multi-voting or other consensus ...
Canada's ruling Liberal Party is looking for a new leader to replace Prime Minister Justin Trudeau, who announced on Monday he intended to step down. Finance Minister Dominic LeBlanc said on ...
Luigi Mangione, the suspect accused of fatally shooting UnitedHealthcare CEO Brian Thompson in New York City last week, was not a customer of the private health insurer, but police say he had ...