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Determinant

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Determinant
Dbpedia
Wikipedia articleDbpedia source
In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. It characterizes some properties of the matrix and the linear map represented by the matrix. In particular, the determinant is nonzero if and only if the matrix is invertible and the linear map represented by the matrix is an isomorphism. The determinant of a product of matrices is the product of their determinants (the preceding property is a corollary of this one).The determinant of a matrix A is denoted det(A), det A, or |A|. In the case of a 2 × 2 matrix the determinant can be defined as Similarly, for a 3 × 3 matrix A, its determinant is Each determinant of a 2 × 2 matrix in this equation is called a minor of the matrix A. This procedure can be extended to give a recursive definition for the determinant of an n × n matrix, known as Laplace expansion. Determinants occur throughout mathematics. For example, a matrix is often used to represent the coefficients in a system of linear equations, and determinants can be used to solve these equations (Cramer's rule), although other methods of solution are computationally much more efficient. Determinants are used for defining the characteristic polynomial of a matrix, whose roots are the eigenvalues. In geometry, the signed n-dimensional volume of a n-dimensional parallelepiped is expressed by a determinant. This is used in calculus with exterior differential forms and the Jacobian determinant, in particular for changes of variables in multiple integrals.
Determinante (matemática)
English Wikipedia http://en.wikipedia.org/wiki/Determinant
Spanish wikipedia http://es.wikipedia.org/wiki/Determinante_(matemática)
Wiki page external link http://algebra.math.ust.hk/course/content.shtml http://ftp.cs.wisc.edu/Approx/empty.pdf http://www.matrixanalysis.com/DownloadChapters.html http://www.umat.feec.vutbr.cz/~novakm/determinanty/en/ https://page.inf.fu-berlin.de/~rote/Papers/pdf/Division-free+algorithms.pdf%7Caccess-date=2020-06-04%7Carchive-date=2007-02-01%7Carchive-url=https:/web.archive.org/web/20070201145100/http:/page.inf.fu-berlin.de/~rote/Papers/pdf/Division-free+algorithms.pdf%7Curl-status=dead https://physandmathsolutions.com/Menus/matrix_determinant_calculator.php https://www.ams.org/journals/mcom/1968-22-103/S0025-5718-1968-0226829-0/S0025-5718-1968-0226829-0.pdf%7Cjournal=Mathematics http://people.revoledu.com/kardi/tutorial/LinearAlgebra/MatrixDeterminant.html https://gallica.bnf.fr/ark:/12148/bpt6k106053p.image https://gallica.bnf.fr/ark:/12148/bpt6k77596b/f374 https://hal.archives-ouvertes.fr/hal-01500199/file/HA.pdf%7Cdoi-access=free https://web.archive.org/web/20081204081902/http:/www.umat.feec.vutbr.cz/~novakm/determinanty/en/ https://web.archive.org/web/20091031193126/http:/matrixanalysis.com/DownloadChapters.html https://www.digizeitschriften.de/dms/img/%3FPID=GDZPPN002142724&physid=phys325%23navi%7Cjournal=Journal http://www.economics.soton.ac.uk/staff/aldrich/matrices.htm

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Fecha publicación: 21.3.2020

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