The envelope of tridiagonal Toeplitz matrices and block-shift matrices

被引：4

作者：

Aretaki, Aik. ^{[1
]}

Psarrakos, P. ^{[1
]}

Tsatsomeros, M. ^{[2
]}

机构：

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

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

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2017年 / 532卷

关键词：

Eigenvalue; Envelope; Cubic curve; Numerical range; Tridiagonal Toeplitz matrix; Block-shift matrix; Jordan block; SPECTRUM; VALUES;

D O I：

10.1016/j.laa.2017.06.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The envelope of a square complex matrix is a spectrum encompassing region in the complex plane. It is contained in and is akin to the numerical range in the sense that the envelope is obtained as an infinite intersection of unbounded regions contiguous to cubic curves, rather than half-planes. In this article, the geometry and properties of the envelopes of special matrices are examined. In particular, symmetries of the envelope of a tridiagonal Toeplitz matrix are obtained, and the envelopes of block-shift matrices, Jordan blocks and 2 x 2 matrices are explicitly characterized. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：60 / 85

页数：26

共 14 条

[1]

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

[2]

Ball W.W. R., 1890, Proc. Lond. Math. Soc, V22, P104

[3]

BOTTCHER A, 2005, SPECTRAL PROPERTIES

[4] CIRCULARITY OF THE NUMERICAL RANGE [J].