Noun
Gaussian elimination (countable and uncountable, plural Gaussian eliminations)
(linear algebra) A method of reducing an augmented matrix to row echelon form.
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. Source: Internet
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. Source: Internet
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. Source: Internet
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. Source: Internet
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. Source: Internet
The Gaussian elimination algorithm remains applicable. Source: Internet