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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 ]
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 .
An "almost" triangular matrix, for example, an upper Hessenberg matrix has zero entries below the first subdiagonal. Hollow matrix: A square matrix whose main diagonal comprises only zero elements. Integer matrix: A matrix whose entries are all integers. Logical matrix: A matrix with all entries either 0 or 1.
b) Sample Hi-C interaction matrix showing genomic compartments along with the calculated compartment value, as given by first principal component analysis. c) Sample Hi-C interaction matrix, rotated by 45 degrees, showing topologically associating domains. Sample Hi-C data only shows 3 chromosomes for simplicity.
College Football Playoff quarterfinals Fiesta Bowl. No. 6 Penn State vs. No. 3 Boise State. Date: Dec. 31 | Time: 7:30 p.m. ET | TV: ESPN | Line: Penn State -10.5 | Total: 52.5 The Nittany Lions ...
WASHINGTON (Reuters) -U.S. manufacturing contracted at a moderate pace in November, with orders growing for the first time in eight months and factories facing significantly lower prices for inputs.
Jacob says that according to police reports, the pastor left the church around 4:15 p.m., while Hazelle stayed behind making copies. That evening, the pastor got a concerning call from Hazelle’s ...