## Abstract

As in the predecessor [Numerical range of a normal compression, Linear and Multilinear Algebra, in press] of this paper, we consider properties of matrices of the form V*NV, where N=diag(a_{1},⋯,a _{n+1}) is a diagonal matrix with distinct eigenvalues a_{j}s such that each of them is a corner of the convex hull they generate, and V is an (n+1)-by-n matrix with V*V=I_{n} such that any nonzero vector orthogonal to the range space of V has all its components nonzero. We obtain that such a matrix A is determined by its eigenvalues up to unitary equivalence, is irreducible and cyclic, and the boundary of its numerical range is a differentiable curve which contains no line segment. We also consider the condition for the existence of another matrix of the above type which dilates to A such that their numerical ranges share some common points with the boundary of the (n+1)-gon a_{1}⋯a_{n+1}.

Original language | English |
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Pages (from-to) | 121-136 |

Number of pages | 16 |

Journal | Linear Algebra and Its Applications |

Volume | 390 |

Issue number | 1-3 |

DOIs | |

State | Published - 1 Oct 2004 |

## Keywords

- Cyclic matrix
- Irreducible matrix
- Normal compression
- Numerical range