Row echelon form

This article defines a property that can be evaluated for a matrix. In other words, given a matrix, the matrix either satisfies or does not satisfy the property.
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Definition

A matrix is said to be a row echelon matrix, or is said to be in row echelon form, if it satisfies the following conditions:

• All nonzero rows are above all zero rows. Here, a nonzero row is a row that has at least one nonzero entry, and a zero row is a row where all entries are zero.
• The first nonzero entry in any nonzero row occurs in a strictly later column than the first nonzero entry in the row immediately above it (and hence also, in all the rows above it).
• The first nonzero entry in any nonzero row is 1 (this condition is omitted in some definitions).

Relation with other properties

Stronger properties

• reduced row echelon form