Gaussian elimination
Noun
Meaning
Gaussian elimination (countable and uncountable, plural Gaussian eliminations)
(linear algebra) A method of reducing an augmented matrix to row echelon form.
Synonyms
Examples
If the Gaussian elimination applied to a square matrix A produces a row echelon matrix B, let d be the product of the scalars by which the determinant has been multiplied, using above rules.
Gaussian elimination does not generalize in any simple way to higher order tensors (matrices are array representations of order 2 tensors); even computing the rank of a tensor of order greater than 2 is a difficult problem.
Determinants could also be used to solve systems of linear equations (see Cramer's rule ), but in real applications, Gaussian elimination is a faster method.
Even on the fastest computers, the elementary methods are impractical for n above 20. Finding the inverse of a matrix seeAlso A variant of Gaussian elimination called Gauss–Jordan elimination can be used for finding the inverse of a matrix, if it exists.
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.
The Gaussian elimination algorithm remains applicable.