# 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.

$$\left(\begin{array}{ccc}\hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 1\hfill \\ \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \end{array}\right)$$ |

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).

Title | basal units |
---|---|

Canonical name | BasalUnits |

Date of creation | 2013-03-22 19:17:13 |

Last modified on | 2013-03-22 19:17:13 |

Owner | pahio (2872) |

Last modified by | pahio (2872) |

Numerical id | 7 |

Author | pahio (2872) |

Entry type | Definition |

Classification | msc 15A03 |

Related topic | MatrixRing |

Related topic | StandardBasis |