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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}
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.
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.
Matrix isolation is an experimental technique used in chemistry and physics. It generally involves a material being trapped within an unreactive matrix. A host matrix is a continuous solid phase in which guest particles (atoms, molecules, ions, etc.) are embedded. The guest is said to be isolated within the host matrix.
Elimination reaction of cyclohexanol to cyclohexene with sulfuric acid and heat [1] An elimination reaction is a type of organic reaction in which two substituents are removed from a molecule in either a one- or two-step mechanism. [2] The one-step mechanism is known as the E2 reaction, and the two-step mechanism is known as the E1 reaction ...
Reductive elimination is an elementary step in organometallic chemistry in which the oxidation state of the metal center decreases while forming a new covalent bond between two ligands. It is the microscopic reverse of oxidative addition, and is often the product-forming step in many catalytic processes. Since oxidative addition and reductive ...
In organic chemistry, the E i mechanism (Elimination Internal/Intramolecular), also known as a thermal syn elimination or a pericyclic syn elimination, is a special type of elimination reaction in which two vicinal (adjacent) substituents on an alkane framework leave simultaneously via a cyclic transition state to form an alkene in a syn elimination. [1]