On eigenvalues and boundary curvature of the numerical range

Lauren Caston; Milena Savova; Ilya Spitkovsky; Nahum Zobin

doi:10.1016/S0024-3795(00)00231-7

On eigenvalues and boundary curvature of the numerical range

Lauren Caston, Milena Savova, Ilya Spitkovsky, Nahum Zobin

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let A be an n×n matrix. By Donoghue's theorem, all corner points of its numerical range W(A) belong to the spectrum σ(A). It is therefore natural to expect that, more generally, the distance from a point p on the boundary ∂W(A) of W(A) to σ(A) should be in some sense bounded by the radius of curvature of ∂W(A) at p. We establish some quantitative results in this direction.

Original language	English (US)
Pages (from-to)	129-140
Number of pages	12
Journal	Linear Algebra and Its Applications
Volume	322
Issue number	1-3
DOIs	https://doi.org/10.1016/S0024-3795(00)00231-7
State	Published - Jan 1 2001

Keywords

Curvature
Eigenvalues
Numerical range
Primary 47A12
Secondary 15A42, 14H50

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/S0024-3795(00)00231-7

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title = "On eigenvalues and boundary curvature of the numerical range",

abstract = "Let A be an n×n matrix. By Donoghue's theorem, all corner points of its numerical range W(A) belong to the spectrum σ(A). It is therefore natural to expect that, more generally, the distance from a point p on the boundary ∂W(A) of W(A) to σ(A) should be in some sense bounded by the radius of curvature of ∂W(A) at p. We establish some quantitative results in this direction.",

keywords = "Curvature, Eigenvalues, Numerical range, Primary 47A12, Secondary 15A42, 14H50",

author = "Lauren Caston and Milena Savova and Ilya Spitkovsky and Nahum Zobin",

note = "Funding Information: {\o} This research was conducted while the first two authors were participating at the College of William and Mary{\textquoteright}s Research Experience for Undergraduates program in the summer of 1999 and was supported by NSF grant DMS-96-19577. M. Savova received support from Mount Holyoke College, and I. Spitkovsky was also supported by NSF grant DMS-98-00704. ∗ Corresponding author. E-mail addresses: caston@math.berkeley.edu (L. Caston), mksavova@mtholyoke.edu (M. Savova), ilya@math.wm.edu (I. Spitkovsky), zobin@math.wm.edu (N. Zobin).",

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doi = "10.1016/S0024-3795(00)00231-7",

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T1 - On eigenvalues and boundary curvature of the numerical range

AU - Caston, Lauren

AU - Savova, Milena

AU - Spitkovsky, Ilya

AU - Zobin, Nahum

N1 - Funding Information: ø This research was conducted while the first two authors were participating at the College of William and Mary’s Research Experience for Undergraduates program in the summer of 1999 and was supported by NSF grant DMS-96-19577. M. Savova received support from Mount Holyoke College, and I. Spitkovsky was also supported by NSF grant DMS-98-00704. ∗ Corresponding author. E-mail addresses: caston@math.berkeley.edu (L. Caston), mksavova@mtholyoke.edu (M. Savova), ilya@math.wm.edu (I. Spitkovsky), zobin@math.wm.edu (N. Zobin).

PY - 2001/1/1

Y1 - 2001/1/1

N2 - Let A be an n×n matrix. By Donoghue's theorem, all corner points of its numerical range W(A) belong to the spectrum σ(A). It is therefore natural to expect that, more generally, the distance from a point p on the boundary ∂W(A) of W(A) to σ(A) should be in some sense bounded by the radius of curvature of ∂W(A) at p. We establish some quantitative results in this direction.

AB - Let A be an n×n matrix. By Donoghue's theorem, all corner points of its numerical range W(A) belong to the spectrum σ(A). It is therefore natural to expect that, more generally, the distance from a point p on the boundary ∂W(A) of W(A) to σ(A) should be in some sense bounded by the radius of curvature of ∂W(A) at p. We establish some quantitative results in this direction.

KW - Curvature

KW - Eigenvalues

KW - Numerical range

KW - Primary 47A12

KW - Secondary 15A42, 14H50

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EP - 140

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1-3

ER -

On eigenvalues and boundary curvature of the numerical range

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Keywords

ASJC Scopus subject areas

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