# Definition:Elementary Matrix/Row Operation

< Definition:Elementary Matrix(Redirected from Definition:Elementary Row Matrix)

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## Definition

Let $\mathbf E$ be a unit matrix on which exactly one elementary row operation $e$ has been performed.

Then $\mathbf E$ is called the **elementary row matrix** for the elementary row operation $e$.

## Also known as

In treatments of linear algebra and matrix theory, it is usual to focus attention on elementary row operations and their associated **elementary row matrices**.

Hence it is usual to use the term **elementary matrix** to mean exclusively an elementary row matrix.

When handling elementary column operations, the full term is then used: **elementary column matrix**.

On $\mathsf{Pr} \infty \mathsf{fWiki}$, where both treatments are discussed, it will be usual to use the full description for both types of **elementary matrix**.

## Also see

- Results about
**elementary matrices**can be found here.

## Sources

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next): Entry:**elementary matrix**(abbrev.**E-matrix**) - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**elementary matrix**