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The name is used because it is a variation of Gaussian elimination as described by Wilhelm Jordan in 1888. However, the method also appears in an article by Clasen published in the same year. Jordan and Clasen probably discovered Gauss–Jordan elimination independently. [9]
Wilhelm Jordan (1 March 1842, Ellwangen, Württemberg – 17 April 1899, Hanover) was a German geodesist who conducted surveys in Germany and Africa and founded the German geodesy journal. Biography [ edit ]
The reduced row echelon form of a matrix is unique and does not depend on the sequence of elementary row operations used to obtain it. The variant of Gaussian elimination that transforms a matrix to reduced row echelon form is sometimes called Gauss–Jordan elimination. A matrix is in column echelon form if its transpose is in row echelon form.
It is possible to solve the resulting linear system directly with Gauss–Jordan elimination, [2] but this is problematic due to the large memory requirement for storing the matrix of the linear system. Another way is to use iterative methods, where the required number of iterations for a given degree of accuracy depends on the strength of ...
This is an accepted version of this page This is the latest accepted revision, reviewed on 28 December 2024. German mathematician, astronomer, geodesist, and physicist (1777–1855) "Gauss" redirects here. For other uses, see Gauss (disambiguation). Carl Friedrich Gauss Portrait by Christian Albrecht Jensen, 1840 (copy from Gottlieb Biermann, 1887) Born Johann Carl Friedrich Gauss (1777-04-30 ...
"The Gauss-Jordan (GJ) method is a variant of Gaussian elimination (GE). It differs in eliminating the unknown equations above the main diagonal as well as below the main diagonal. The Gauss-Jordan method is equivalent to the use of reduced row echelon form of linear algebra texts. GJ requires 50% more multiplication and division operation than ...
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In mathematics, an elementary matrix is a square matrix obtained from the application of a single elementary row operation to the identity matrix.The elementary matrices generate the general linear group GL n (F) when F is a field.