Linear and multilinear algebra; matrix theory Definition

Row echelon form

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Definition

Let $F$ be a field and let $A$ be an $m \times n$ matrix over $F$ . The leading entry of a nonzero row of $A$ is its first nonzero entry, from the left. The matrix $A$ is in row echelon form when these two conditions hold:

Each zero row of $A$ is below each nonzero row of $A$ .
For two consecutive nonzero rows, the leading entry of the lower row is strictly to the right of the leading entry of the upper row.

Remarks

The matrix $\begin{pmatrix} 1 & 2 & 3 \\ 0 & 0 & 4 \\ 0 & 0 & 0 \end{pmatrix}$ is in row echelon form. Some authors also require that each leading entry is $1$ . In row echelon form, all the entries below a leading entry are zero. Gaussian elimination changes each matrix into a row echelon form by elementary row operations.

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Matrix definition
Row echelon form definition

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Tag	`0F27PBRWD7`
URI	`m2://0F27PBRWD7`
Kind	definition
Writing	W0 stub
MSC	15A06
Defines	Row echelon form
Uses	Matrix

Row echelon form

Definition

Remarks

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