Desnanot-jacobi Identity
In mathematics, Dodgson condensation or method of contractants is a method of computing the determinants of square matrices. It is named for its inventor, Charles Lutwidge Dodgson (better known by his pseudonym, as Lewis Carroll, the popular author). 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. General method This algorithm can be described in the following four steps: # Let A be the given ''n'' × ''n'' matrix. Arrange A so that no zeros occur in its interior. An explicit definition of interior would be all ai,j with i,j\ne1,n. One can do this using any operation that one could normally perform without changing the value of the determinant, such as adding a multiple of one row to another. # Cr ...
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Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ...
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