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- Gaussian_elimination abstract "In linear algebra, Gaussian elimination (also known as row reduction) is an algorithm for solving systems of linear equations. It is usually understood as a sequence of operations performed on the associated matrix of coefficients. This method can also be used to find the rank of a matrix, to calculate the determinant of a matrix, and to calculate the inverse of an invertible square matrix. The method is named after Carl Friedrich Gauss, although it was known to Chinese mathematicians as early as 179 AD (see History section).To perform row reduction on a matrix, one uses a sequence of elementary row operations to modify the matrix until the lower left-hand corner of the matrix is filled with zeros, as much as is possible. There are three types of elementary row operations: 1) Swapping two rows, 2) Multiplying a row by a non-zero number, 3) Adding a multiple of one row to another row. Using these operations, a matrix can always be transformed into an upper triangular matrix, and in fact one that is in row echelon form. Once all of the leading coefficients (the left-most non-zero entry in each row) are 1, and in every column containing a leading coefficient has zeros elsewhere, the matrix is said to be in reduced row echelon form. This final form is unique; in other words, it is independent of the sequence of row operations used. For example, in the following sequence of row operations (where multiple elementary operations might be done at each step), the third and fourth matrices are the ones in row echelon form, and the final matrix is the unique reduced row echelon form.Using row operations to convert a matrix into reduced row echelon form is sometimes called Gauss–Jordan elimination. Some authors use the term Gaussian elimination to refer to the process until it has reached its upper triangular, or (non-reduced) row echelon form. For computational reasons, when solving systems of linear equations, it is sometimes preferable to stop row operations before the matrix is completely reduced.".
- Gaussian_elimination wikiPageExternalLink index.html?pg=46.
- Gaussian_elimination wikiPageExternalLink gauss.cgi.
- Gaussian_elimination wikiPageExternalLink numericalmethods.eng.usf.edu.
- Gaussian_elimination wikiPageExternalLink gaussian_elimination.html.
- Gaussian_elimination wikiPageExternalLink RREF.
- Gaussian_elimination wikiPageExternalLink sole.ooz.ie.
- Gaussian_elimination wikiPageExternalLink rtx110600782p.pdf.
- Gaussian_elimination wikiPageExternalLink www.autarkaw.com.
- Gaussian_elimination wikiPageExternalLink numalg.
- Gaussian_elimination wikiPageExternalLink gauss_jordan.php.
- Gaussian_elimination wikiPageExternalLink spip.php?article53.
- Gaussian_elimination wikiPageExternalLink chapter6.htm.
- Gaussian_elimination wikiPageExternalLink GaussElimination.html.
- Gaussian_elimination wikiPageID "13035".
- Gaussian_elimination wikiPageRevisionID "606746459".
- Gaussian_elimination hasPhotoCollection Gaussian_elimination.
- Gaussian_elimination id "u-AhI4gNB_E".
- Gaussian_elimination title "WildLinAlg13: Solving a system of linear equations".
- Gaussian_elimination subject Category:Articles_with_example_pseudocode.
- Gaussian_elimination subject Category:Exchange_algorithms.
- Gaussian_elimination subject Category:German_inventions.
- Gaussian_elimination subject Category:Numerical_linear_algebra.
- Gaussian_elimination type Abstraction100002137.
- Gaussian_elimination type Act100030358.
- Gaussian_elimination type Activity100407535.
- Gaussian_elimination type Algorithm105847438.
- Gaussian_elimination type Event100029378.
- Gaussian_elimination type ExchangeAlgorithms.
- Gaussian_elimination type Procedure101023820.
- Gaussian_elimination type PsychologicalFeature100023100.
- Gaussian_elimination type Rule105846932.
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- Gaussian_elimination comment "In linear algebra, Gaussian elimination (also known as row reduction) is an algorithm for solving systems of linear equations. It is usually understood as a sequence of operations performed on the associated matrix of coefficients. This method can also be used to find the rank of a matrix, to calculate the determinant of a matrix, and to calculate the inverse of an invertible square matrix.".
- Gaussian_elimination label "Eliminação de Gauss".
- Gaussian_elimination label "Gauss-eliminatie".
- Gaussian_elimination label "Gaussian elimination".
- Gaussian_elimination label "Gaußsches Eliminationsverfahren".
- Gaussian_elimination label "Metoda eliminacji Gaussa".
- Gaussian_elimination label "Metodo di eliminazione di Gauss".
- Gaussian_elimination label "Метод Гаусса".
- Gaussian_elimination label "حذف غاوسي".
- Gaussian_elimination label "ガウスの消去法".
- Gaussian_elimination label "高斯消去法".
- Gaussian_elimination sameAs Gaussova_eliminační_metoda.
- Gaussian_elimination sameAs Gaußsches_Eliminationsverfahren.
- Gaussian_elimination sameAs Metodo_di_eliminazione_di_Gauss.
- Gaussian_elimination sameAs ガウスの消去法.
- Gaussian_elimination sameAs 가우스_소거법.
- Gaussian_elimination sameAs Gauss-eliminatie.
- Gaussian_elimination sameAs Metoda_eliminacji_Gaussa.
- Gaussian_elimination sameAs Eliminação_de_Gauss.
- Gaussian_elimination sameAs m.03dv7.
- Gaussian_elimination sameAs Q2658.
- Gaussian_elimination sameAs Q2658.
- Gaussian_elimination sameAs Gaussian_elimination.
- Gaussian_elimination wasDerivedFrom Gaussian_elimination?oldid=606746459.
- Gaussian_elimination isPrimaryTopicOf Gaussian_elimination.