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## 摘要

The zero-dilation index d(A) of a square matrix A is the largest k for which A is unitarily similar to a matrix of the form (Formula presented), where 0_{k} denotes the k-by-k zero matrix. In this paper, it is shown that if A is an Sn-matrix or an n-by-n companion matrix, then d(A) is at most [n/2], the smallest integer greater than or equal to n/2. Those A’s for which the upper bound is attained are also characterized. Among other things, it is shown that, for an odd n, the S_{n}-matrix A is such that d(A) = (n+1)/2 if and only if A is unitarily similar to -A, and, for an even n, every n-by-n companion matrix A has d(A) equal to n/2.

原文 | ???core.languages.en_GB??? |
---|---|

文章編號 | 47 |

頁（從 - 到） | 666-678 |

頁數 | 13 |

期刊 | Electronic Journal of Linear Algebra |

卷 | 31 |

發行號 | 1 |

DOIs | |

出版狀態 | 已出版 - 2016 |

## 指紋

深入研究「Zero-dilation index of S_{n}-matrix and companion matrix」主題。共同形成了獨特的指紋。

## 專案

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