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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.
The other elimination pathways are less important in the elimination of drugs, except in very specific cases, such as the respiratory tract for alcohol or anaesthetic gases. The case of mother's milk is of special importance. The liver and kidneys of newly born infants are relatively undeveloped and they are highly sensitive to a drug's toxic ...
For a symmetric matrix A, the vector vec(A) contains more information than is strictly necessary, since the matrix is completely determined by the symmetry together with the lower triangular portion, that is, the n(n + 1)/2 entries on and below the main diagonal.
For a (not necessarily invertible) matrix over any field, the exact necessary and sufficient conditions under which it has an LU factorization are known. The conditions are expressed in terms of the ranks of certain submatrices. The Gaussian elimination algorithm for obtaining LU decomposition has also been extended to this most general case. [11]
It deals with the influence of acquired and inherited genetic variation on drug response, by correlating DNA mutations (including point mutations, copy number variations, and structural variations) with pharmacokinetic (drug absorption, distribution, metabolism, and elimination), pharmacodynamic (effects mediated through a drug's biological ...
Exon shuffling is a molecular mechanism for the formation of new genes. It is a process through which two or more exons from different genes can be brought together ectopically, or the same exon can be duplicated, to create a new exon-intron structure. [1]
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.
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 ...