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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 pharmacology, clearance is a pharmacokinetic parameter representing the efficiency of drug elimination. This is the rate of elimination of a substance divided by its concentration. [ 1 ] The parameter also indicates the theoretical volume of plasma from which a substance would be completely removed per unit time.
An example of a Levey–Jennings chart with upper and lower limits of one and two times the standard deviation. A Levey–Jennings chart is a graph that quality control data is plotted on to give a visual indication whether a laboratory test is working well. The distance from the mean is measured in standard deviations.
For example, we might swap rows to perform partial pivoting, or we might do it to set the pivot element , on the main diagonal to a non-zero number so that we can complete the Gaussian elimination. For our matrix (), we want to set every element below , to zero (where , is the element in the n-th column of the main diagonal).
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 .
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 ...
choices. The primary example of such information-based legislation is the Nutrition Labeling and Education Act (NLEA), which was implemented in 1994 (United States Food and Drug Administration) and required that consumers have access to consistent nutritional information for packaged foods.
The reduced row echelon form of a matrix is unique and does not depend on the sequence of elementary row operations used to obtain it. The variant of Gaussian elimination that transforms a matrix to reduced row echelon form is sometimes called Gauss–Jordan elimination. A matrix is in column echelon form if its transpose is in