线性代数中，一个矩阵如果符合下列条件的话，我们称之为行阶梯形矩阵'（Row Echelon Form）：

这个3×4矩阵是行阶梯形矩阵：

有时候，增广矩阵右边的直线也会省略。

In linear algebra, a matrix is in echelon form if it has the shape resulting from a Gaussian elimination. Row echelon form means that Gaussian elimination has operated on the rows and column echelon form means that Gaussian elimination has operated on the columns. In other words, a matrix is in column echelon form if its transpose is in row echelon form. Therefore only row echelon forms are considered in the remainder of this article. The similar properties of column echelon form are easily deduced by transposing all the matrices.