## You are here

Homebasal units

## Primary tabs

# basal units

The set of all $n\!\times\!n$ matrices over a skew field forms an $n^{2}$-dimensional associative algebra, for the basis of which one can take the *basal units*. A basal unit of the algebra has all components zeroes except only one which is 1.

E.g.

$\begin{pmatrix}0&0&0\\ 0&0&1\\ 0&0&0\end{pmatrix}$ |

is a basal unit of the algebra of $3\!\times\!3$ matrices.

# References

- 1 L. E. Dickson: Algebras and their arithmetics. Dover Publications, Inc. New York (1923; second edition 1960).

Related:

MatrixRing, StandardBasis

Type of Math Object:

Definition

Major Section:

Reference

Parent:

Groups audience:

## Mathematics Subject Classification

15A03*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections