Definition:Gauss-Jordan Elimination
Definition
Gauss-Jordan elimination is a variant of Gaussian elimination whose effect is to reduce a given matrix $\mathbf A$ to diagonal form.
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Also see
- Results about Gauss-Jordan elimination can be found here.
Source of Name
This entry was named for Carl Friedrich Gauss and Wilhelm Jordan.
Historical Note
Gauss-Jordan elimination was invented by Wilhelm Jordan as a variant of Gaussian elimination.
As a means of solving a system of simultaneous equations $\mathbf A \mathbf x = \mathbf b$, Gaussian elimination is preferred, as it requires much less work.
When used to calculate the inverse of a square matrix, Gauss-Jordan elimination is sometimes used instead of Gaussian elimination, as they take the same amount of work.
By applying a final scaling in which each non-zero row is divided by its first non-zero element, Gauss-Jordan elimination can be applied to am $m \times n$ matrix to obtain its reduced row echelon form.
Sources
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Gauss-Jordan elimination