Definition:Elementary Matrix/Row Operation

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

• Definition:Elementary Row Operation

• Definition:Elementary Column Matrix

• Results about elementary matrices can be found here.

Sources

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