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In mathematics, Gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations. It consists of a sequence of row-wise operations performed on the corresponding matrix of coefficients. This method can also be used to compute the rank of a matrix, the determinant of a square matrix, and the inverse of ...
Rules of inference. Implication introduction / elimination (modus ponens) Biconditional introduction / elimination. Conjunction introduction / elimination. Disjunction introduction / elimination. Disjunctive / hypothetical syllogism. Constructive / destructive dilemma.
Elementary matrix. In mathematics, an elementary matrix is a matrix which differs from the identity matrix by one single elementary row operation. The elementary matrices generate the general linear group GLn(F) when F is a field. Left multiplication (pre-multiplication) by an elementary matrix represents elementary row operations, while right ...
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In propositional logic, conjunction elimination (also called and elimination, ∧ elimination, [1] or simplification) [2] [3] [4] is a valid immediate inference, argument form and rule of inference which makes the inference that, if the conjunction A and B is true, then A is true, and B is true. The rule makes it possible to shorten longer ...
Duplication and elimination matrices. 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.
Arrow pushing or electron pushing is a technique used to describe the progression of organic chemistry reaction mechanisms. It was first developed by Sir Robert Robinson.In using arrow pushing, "curved arrows" or "curly arrows" are drawn on the structural formulae of reactants in a chemical equation to show the reaction mechanism.
Addition–elimination reaction. In chemistry, an addition-elimination reaction is a two- step reaction process of an addition reaction followed by an elimination reaction. This gives an overall effect of substitution, and is the mechanism of the common nucleophilic acyl substitution often seen with esters, amides, and related structures.
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