### 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 | |

State | Published - Jan 1 2001 |

### Fingerprint

### 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

### Cite this

*Linear Algebra and Its Applications*,

*322*(1-3), 129-140. https://doi.org/10.1016/S0024-3795(00)00231-7

**On eigenvalues and boundary curvature of the numerical range.** / Caston, Lauren; Savova, Milena; Spitkovsky, Ilya; Zobin, Nahum.

Research output: Contribution to journal › Article

*Linear Algebra and Its Applications*, vol. 322, no. 1-3, pp. 129-140. https://doi.org/10.1016/S0024-3795(00)00231-7

}

TY - JOUR

T1 - On eigenvalues and boundary curvature of the numerical range

AU - Caston, Lauren

AU - Savova, Milena

AU - Spitkovsky, Ilya

AU - Zobin, Nahum

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

UR - http://www.scopus.com/inward/record.url?scp=0035578974&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035578974&partnerID=8YFLogxK

U2 - 10.1016/S0024-3795(00)00231-7

DO - 10.1016/S0024-3795(00)00231-7

M3 - Article

VL - 322

SP - 129

EP - 140

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - 1-3

ER -