Principal powers of matrices with positive definite real part

被引：56

作者：

Drury, Stephen ^{[1
]}

机构：

[1] McGill Univ, Dept Math & Stat, Montreal, PQ, Canada

来源：

LINEAR & MULTILINEAR ALGEBRA | 2015年 / 63卷 / 02期

关键词：

principal power; operator norm; geometric mean; symbolic calculus; numerical range; 15A45;

D O I：

10.1080/03081087.2013.865732

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study principal powers of complex square matrices with positive definite real part, or with numerical range contained in a sector. We extend the notion of geometric mean to such matrices and we establish an operator norm bound in this context.

引用

页码：296 / 301

页数：6

共 8 条

[1]

Bhatia R, 2007, PRINC SER APPL MATH, P1

[2] Numerical ranges of the powers of an operator [J].

Choi, Man-Duen ;

Li, Chi-Kwong .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 365 (02) :458-466

[3] Fischer determinantal inequalities and Higham's Conjecture [J].

Drury, S. W. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2013, 439 (10) :3129-3133

[4]

Drury SW, PREPRINT

[5]

Drury SW, 2013, LINEAR MULTILINEAR A, DOI [10.1080/03081087.2013.832244, DOI 10.1080/03081087.2013.832244.]

[6] On the properties of accretive-dissipative matrices [J].

George, A ;

Ikramov, KD .

MATHEMATICAL NOTES, 2005, 77 (5-6) :767-776

[7]

Gradshteyn L.S., 1980, Tables of Integrals, Series, and Products, P837

[8]

Li C-K, J MATH ANAL APPL

← 1 →