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→(General) row echelon form: Confusing and non-standard to refer to Row echelon form as "General", i.e. implying Reverse echelon form is a special case |
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In [[linear algebra]], a [[Matrix (mathematics)|matrix]] is in '''row echelon form''' if it can be obtained as the result of [[Gaussian elimination]]. Every matrix can be put in row echelon form by applying a sequence of [[elementary row operation]]s. The term ''echelon'' comes from the French ''échelon'' ("level" or step of a ladder), and refers to the fact that the nonzero entries of a matrix in row echelon form look like an inverted staircase.
[[File:Row echelon form.png|thumb|right|Example of a rectangular matrix in row echelon form]]
For [[square matrices]], an [[upper triangular matrix]] with nonzero entries on the diagonal is in row echelon form, and a matrix in row echelon form is (weakly) upper triangular. Thus, the row echelon form can be viewed as a generalization of upper triangular form for rectangular matrices.
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