An envelope for the spectrum of a matrix

被引：7

作者：

Psarrakos, Panayiotis J. ^{[1
]}

Tsatsomeros, Michael J. ^{[2
]}

机构：

[1] Natl Tech Univ Athens, Dept Math, Athens 15780, Greece

[2] Washington State Univ, Dept Math, Pullman, WA 99164 USA

来源：

CENTRAL EUROPEAN JOURNAL OF MATHEMATICS | 2012年 / 10卷 / 01期

关键词：

Eigenvalue bounds; Numerical range; Cubic curve; SKEW-SYMMETRIC MATRICES; NUMERICAL RANGE; INEQUALITY;

D O I：

10.2478/s11533-011-0111-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce and study an envelope-type region E >(A) in the complex plane that contains the eigenvalues of a given nxn complex matrix A. E >(A) is the intersection of an infinite number of regions defined by cubic curves. The notion and method of construction of E >(A) extend the notion of the numerical range of A, F(A), which is known to be an intersection of an infinite number of half-planes; as a consequence, E >(A) is contained in F(A) and represents an improvement in localizing the spectrum of A.

引用

页码：292 / 302

页数：11

共 10 条

[1]

Adam M, 2006, ELECTRON J LINEAR AL, V15, P239

[2]

[Anonymous], 1991, TOPICS MATRIX ANAL, DOI DOI 10.1017/CBO9780511840371

[3]

[Anonymous], 2006, Elliptic Curves

[4] On flat portions on the boundary of the numerical range [J].

Brown, ES ;

Spitkovsky, IA .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2004, 390 :75-109

[5] NUMERICAL DETERMINATION OF FIELD OF VALUES OF A GENERAL COMPLEX MATRIX [J].

JOHNSON, CR .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1978, 15 (03) :595-602

[6]

LEVINGER BW, 1970, NOT AM MATH SOC, V17, P260

[7] Almost skew-symmetric matrices [J].

McDonald, JJ ;

Psarrakos, PJ ;

Tsatsomeros, MJ .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2004, 34 (01) :269-288

[8] Bounds for Levinger's function of nonnegative almost skew-symmetric matrices [J].

Psarrakos, Panayiotis J. ;

Tsatsomeros, Michael J. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2006, 416 (2-3) :759-772

[9] The block numerical range of an n x n block operator matrix [J].

Tretter, C ;

Wagenhofer, M .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2003, 24 (04) :1003-1017

[10]

Tretter C., 2008, SPECTRAL THEORY BLOC, DOI DOI 10.1142/P493

← 1 →