Rings and groups of matrices with a nonstandard product

被引：6

作者：

Bardakov, V. G. ^{[1
]}

Simonov, A. A. ^{[1
]}

机构：

[1] Novosibirsk State Univ, Sobolev Inst Math, Novosibirsk 630090, Russia

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2013年 / 54卷 / 03期

关键词：

product of matrices; group of matrices; generalized matrix multiplication;

D O I：

10.1134/S0037446613030038

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We define a new operation of multiplication on the set of square matrices. We determine when this multiplication is associative and when the set of matrices with this multiplication and the ordinary addition of matrices constitutes a ring. Furthermore, we determine when the nonstandard product admits the identity element and which elements are invertible. We study the relation between the nonstandard product and the affine transformations of a vector space. Using these results, we prove that the MikhaAlichenko group, which is a group of matrices with the nonstandard product, is isomorphic to a subgroup of matrices of a greater size with the ordinary product.

引用

页码：393 / 405

页数：13