# 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).
Title basal units BasalUnits 2013-03-22 19:17:13 2013-03-22 19:17:13 pahio (2872) pahio (2872) 7 pahio (2872) Definition msc 15A03 MatrixRing StandardBasis