摘要
在多复变分析的研究中,华罗庚(1955年)发现并证明了行列式不等式:如果n×n复矩阵A,B满足I-AAH,I-BBH都是正定矩阵,则det(I-AAH)det(I-BBH)+det(A-B)2 det(I-ABH)2,仅当A=B时取等号.我们给出了华罗庚行列式不等式的等式成立的充分必要条件.
In the study of the of functions of several complex variables, Hua Loo-Keng discovered and proved the following determinant inequality ： If A, B are n × n complex matrices and I - AA^H and I - BB^H are Hermitian positive definite matrices, then det（I-AA^H）det（I-BB^H）＋│det（A-B）│^2≤│det（I-AB^H）│^2 with equality only if A = B.
In this paper, necessary and sufficient conditions that the equality holds for Hua Loo-Keng inequality of determinant are presented.
出处
《数学的实践与认识》
CSCD
北大核心
2006年第4期222-225,共4页
Mathematics in Practice and Theory
基金
福建省自然科学基金(Z0511051)
莆田学院科研项目(2004Q002)
关键词
复矩阵
行列式
不等式
等式条件
complex matrices
determinant
inequality
equality condition
