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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 ]
This real Jordan form is a consequence of the complex Jordan form. For a real matrix the nonreal eigenvectors and generalized eigenvectors can always be chosen to form complex conjugate pairs. Taking the real and imaginary part (linear combination of the vector and its conjugate), the matrix has this form with respect to the new basis.
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.
In mathematics, the Bruhat decomposition (introduced by François Bruhat for classical groups and by Claude Chevalley in general) = of certain algebraic groups = into cells can be regarded as a general expression of the principle of Gauss–Jordan elimination, which generically writes a matrix as a product of an upper triangular and lower triangular matrices—but with exceptional cases.
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 ...
Pages for logged out editors learn more. Contributions; Talk; Gauss-Jordan elimination
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.