### 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 |

### 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

## Fingerprint Dive into the research topics of 'On eigenvalues and boundary curvature of the numerical range'. Together they form a unique fingerprint.

## Cite this

Caston, L., Savova, M., Spitkovsky, I., & Zobin, N. (2001). On eigenvalues and boundary curvature of the numerical range.

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