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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.
In chemical analysis, matrix refers to the components of a sample other than the analyte [1] of interest. The matrix can have a considerable effect on the way the analysis is conducted and the quality of the results are obtained; such effects are called matrix effects. [ 2 ]
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.
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"
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.
Man, I wish @PatMcAfeeShow would’ve let him keep going! It just got good. I don’t know about the Vax stuff, but shoot he almost put a name on it. It’s a lapel pin BTW!! 😂😂😂😂 ...
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 ...
Improvement to cognitive performance caused by exercise could last for 24 hours, a new study shows. Scientists also linked getting 6 or more hours of sleep to better memory test scores the next day.