Extensions of Fischer's inequality

被引：13

作者：

Choi, Daeshik ^{[1
]}

Tam, Tin-Yau ^{[2
]}

Zhang, Pingping ^{[3
]}

机构：

[1] Lake Super State Univ, Sch Math & Comp Sci, Sault Sainte Marie, MI 49783 USA

[2] Univ Nevada, Dept Math & Stat, Reno, NV 89557 USA

[3] Chongqing Univ Posts & Telecommun, Sch Sci, Chongqing 400065, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2019年 / 569卷

基金：

中国国家自然科学基金;

关键词：

Fischer's inequality; Numerical range in a sector; Determinants of block matrices; MATRICES;

D O I：

10.1016/j.laa.2019.01.022

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Denote by B(n(1), ..., n(k)) the set of block matrices whose (i, j)-blocks are n(i) x n(j) complex matrices. Let A(i) is an element of B(n(1), ..., n(k)) be positive semidefinite and D-i is an element of B(n(1), ..., n(k)) be block diagonal matrices for 1 <= i <= m. We obtain the following extension of Fischer's inequality: det (Sigma(m)(i=1) D(i)A(i)(pi) D-i(*)) <= Pi(k)(j=1) det (Sigma(m)(i=1)[D-i](j)[A(i)](j)(pi)[D-i](j)(*), 0 <= p(i) <= 1, where [A(i)](j) is the j-th main diagonal block of A(i). In addition, if A(i) and D-i, are nonsingular, the reverse inequality holds when -1 <= p(i) <= 0. We also extend these two results to a larger class of matrices, namely, matrices whose numerical ranges are contained in a sector. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：311 / 322

页数：12