## Abstract

For a given set of n×n matrices F, we study the union of the C-numerical ranges of the matrices in the set F, denoted by W_{C}(F). We obtain basic algebraic and topological properties of W_{C}(F), and show that there are connections between the geometric properties of W_{C}(F) and the algebraic properties of C and the matrices in F. Furthermore, we consider the starshapedness and convexity of the set W_{C}(F). In particular, we show that if F is the convex hull of two matrices such that W_{C}(A) and W_{C}(B) are convex, then the set W_{C}(F) is star-shaped. We also investigate the extensions of the results to the joint C-numerical range of an m-tuple of matrices.

Original language | English |
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Pages (from-to) | 24-46 |

Number of pages | 23 |

Journal | Linear Algebra and Its Applications |

Volume | 563 |

DOIs | |

Publication status | Published - 15 Feb 2019 |

## Keywords

- Convex set
- Numerical range
- Star-shaped set

## ASJC Scopus subject areas

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