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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.
Process of elimination is a logical method to identify an entity of interest among several ones by excluding all other entities. In educational testing , it is a process of deleting options whereby the possibility of an option being correct is close to zero or significantly lower compared to other options.
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.
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 ...
Duplication, or doubling, multiplication by 2; Duplication matrix, a linear transformation dealing with half-vectorization; Doubling the cube, a problem in geometry also known as duplication of the cube; A type of multiplication theorem called the Legendre duplication formula or simply "duplication formula"
Three teens face charges after a Marta bus driver, identified as Leroy Ramos, was killed, officials say.
The problem, they say, is Macy’s is sitting on real estate that is more valuable than the company itself — an untenable situation that masks the true value of the company. Macy’s struggles ...
Inflation heated back up again in November, but it likely wasn’t bad enough to keep the Federal Reserve from cutting rates next week. Consumer prices were up 2.7% for the 12 months ended in ...