C. L. Dodgson. Search for more papers by this author. @MISC{Salem07condensationof, author = {Abdelmalek Salem and Kouachi Said}, title = {CONDENSATION OF DETERMINANTS}, year = {2007}} Share. Title: Condensation of Determinants. In this paper we tried to condense the determinant of n square matrix to the determinant of (n − 1) square matrix with the mathematical proof. OpenURL . This method is uncomplicated by the calculation of 2×2 determinants and unique utilization of matrix condensation techniques which has promise for parallel computing architectures. A a c b d = ⎛ ⎝⎜ ⎞ ⎠⎟, Lewis Carroll’s Condensation Method for Evaluating Determinants “Although more of a recreational mathematician than a serious His paper documented a new method to calculate determinants that was based on Jacobi’s Theorem. Google Scholar. Find this author on PubMed. Given that both determinants are from the same condensation line, they both are reduced by the same akk values. If in computing a certain determinant the maximum of the exponents of all the divisors det(C) is e, we say that the condensation error of that determinant is e. For example, for minors up to size 2 by 2, the condensation error is always 0 since there are never any divisions by quantities with exponent larger than 0. This allows the algorithm to simply discard the akk values in the final computations. Condensation of determinants, being a new and brief method for computing their arithmetical values. The condensation method Google Scholar. Sardar Anisul Haque (UWO) Determinant Computation on the GPU using the Condensation MeAMMCS 2011 4 / 1thod It is named for its inventor Charles Dodgson (better known as Lewis Carroll ). These results suggest that the influence of site characteristics, microhabitats, and regional climate on the formation of condensation water should attract more attention and that both ‐ the relative importance of, and the interactions among different determining factors will contribute to a better understanding of the mechanistic determinants for the formation of condensation water in arid areas. Calculate the determinant for every submatrix of 4 adjacent elements of to form the matrix . determinants of lower degree by taking the product of any row or column entry and the determinant of its complementary minor, then alternately adding and subtracting the results. Aldol condensation is an organic reaction in which an enolate ion reacts with carboxyl compound in order to form a β– hydroxy aldehyde or β– hydroxy ketone. Conjecture 1. The (Dodgson) Condensation Method for Calculating Determinants of Square Matrices Use elementary row operations to remove all zeros from the interior of . The condensation method is presented and proven here, and is demonstrated by a series of examples. The method in the case of an n × n matrix is to construct an ( n − 1) × ( n − 1)matrix, an ( n − 2) × ( n − 2), and so on, finishing with a 1 × 1 matrix, which has one entry, the determinant of the original matrix. evaluating determinants called the condensation method. The akk values factored out during Chio’s condensation cancel during the application of Cramer’s rule. C. L. Dodgson. Hydroxide functions as a base and therefore moves the acidic a-hydrogen producing the reactive enolate ion. For the calculation of determinants, the Dodgson’s determinant condensation algorithm was recently revisited in many papers [ 1, 5, 9, 10]. Find this author on PubMed. Abstract. In mathematics, Dodgson condensation is a method of computing the determinants of square matrices. Search for more papers by this author. 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