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).

随便看

数学辞典收录了18232条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。