Determinant preserving maps on matrix algebras

被引：45

作者：

Dolinar, G

Semrl, P

机构：

[1] Univ Ljubljana, Dept Math, SI-1000 Ljubljana, Slovenia

[2] Univ Ljubljana, Fac Elect Engn, SI-1000 Ljubljana, Slovenia

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2002年 / 348卷 / 1-3期

关键词：

determinant; preserver;

D O I：

10.1016/S0024-3795(01)00578-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let M, be the algebra of all n x n complex matrices. If Phi:M-n-->M-n is a surjective mapping satisfying det(A+lambdaB)=det(phi(A)+lambdaphi(B)). A,B is an element of M-n, lambda is an element of C, then either phi is of the form phi(A)=MAN. A is an element of M-n, or phi is of the form phi(A)=MA(t)N, A is an element of M-n, where M, N is an element of M are nonsingular matrices with det(MN)=1. (C) 2002 Elsevier Science Inc. All rights reserved.

引用

页码：189 / 192

页数：4