M-P invertible matrices and unitary groups over Fq2

被引：0

作者：

Dai, ZD ^{[1
]}

Wan, ZX

机构：

[1] Chinese Acad Sci, Grad Sch, State Key Lab Informat Secur, Beijing 100039, Peoples R China

[2] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China

来源：

SCIENCE IN CHINA SERIES A-MATHEMATICS | 2002年 / 45卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Moor-Penrose generalized inverse; finite field; unitary group;

D O I：

10.1007/BF02872332

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Moor-Penrose generalized inverses (M-P inverses for short) of matrices over a finite field F-q2, which is a generalization of the Moor-Penrose generalized inverses over the complex field, are studied in the present paper. Some necessary and sufficient conditions for an m x n matrix A over Fq2 having an M-P inverse are obtained, which make clear the set of m x n matrices over F-q2 having M-P inverses and reduce the problem of constructing and enumerating the M-P invertible matrices to that of constructing and enumerating the non-isotropic subspaces with respect to the unitary group. Based on this reduction, both the construction problem and the enumeration problem are solved by borrowing the results in geometry of unitary groups over finite fields.

引用

页码：443 / 449

页数：7