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
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