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## Abstract

We show that if A = [a_{ij}]^{n}_{i, j=1} is an n-by-n complex matrix and A′ = [a′_{i,j}]^{n}_{i, j=1}, where (eqution found), then w(A)≥ w(A′), where w(·) denotes the numerical radius of a matrix. Moreover, if n is odd and a_{12},…,a_{n}_{−1,n,}a_{n1} are all nonzero, then w(A) = w(A′) if and only if A = A′. For an even n, under the same nonzero assumption, we have W(A) =W(A′) if and only if A = A′, where W(·) is the numerical range of a matrix.

Original language | English |
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Pages (from-to) | 999-1014 |

Number of pages | 16 |

Journal | Operators and Matrices |

Volume | 11 |

Issue number | 4 |

DOIs | |

State | Published - Dec 2017 |

## Keywords

- Numerical radius
- Numerical range

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Dive into the research topics of 'Lower bounds for the numerical radius'. Together they form a unique fingerprint.## Projects

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