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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.
A matrix effect value of less than 100 indicates suppression, while a value larger than 100 is a sign of matrix enhancement. An alternative definition of matrix effect utilizes the formula: M E = 100 ( A ( e x t r a c t ) A ( s t a n d a r d ) ) − 100 {\displaystyle ME=100\left({\frac {A(extract)}{A(standard)}}\right)-100}
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.
In this one-compartment model, the most common model of elimination is first order kinetics, where the elimination of the drug is directly proportional to the drug's concentration in the organism. This is often called linear pharmacokinetics , as the change in concentration over time can be expressed as a linear differential equation d C d t ...
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 ...
In other sustained release formulations the matrix swells to form a gel through which the drug exits. Another method by which sustained release is achieved is through an osmotic controlled-release oral delivery system , where the active compound is encased in a water-permeable membrane with a laser drilled hole at one end.
Biological half-life (elimination half-life, pharmacological half-life) is the time taken for concentration of a biological substance (such as a medication) to decrease from its maximum concentration (C max) to half of C max in the blood plasma.
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.