On the unitary orbit of complex matrices

Fan Ding; Xingzhi Zhan

doi:10.1137/S0895479800381598

On the unitary orbit of complex matrices

Fan Ding^*
, Xingzhi Zhan

^*Corresponding author for this work

Peking University

Research output: Contribution to journal › Article › peer-review

Abstract

Let M_n(ℂ) be the algebra of n × n complex matrices. Suppose S ⊂ ℂ is a measure zero set. It is proved that if A ∈ M_n(ℂ) is not essentially Hermitian then for almost all unitary matrices U ∈ M_c(ℂ), each entry of U* AU is not in S. Some other results of this type are obtained. The ideas here are mainly from differential topology.

Original language	English
Pages (from-to)	511-516
Number of pages	6
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	23
Issue number	2
DOIs	https://doi.org/10.1137/S0895479800381598
State	Published - 2002
Externally published	Yes

Keywords

Complex matrices
Real analytic map
Unitary orbit

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10.1137/S0895479800381598

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abstract = "Let Mn(ℂ) be the algebra of n × n complex matrices. Suppose S ⊂ ℂ is a measure zero set. It is proved that if A ∈ Mn(ℂ) is not essentially Hermitian then for almost all unitary matrices U ∈ Mc(ℂ), each entry of U* AU is not in S. Some other results of this type are obtained. The ideas here are mainly from differential topology.",

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AB - Let Mn(ℂ) be the algebra of n × n complex matrices. Suppose S ⊂ ℂ is a measure zero set. It is proved that if A ∈ Mn(ℂ) is not essentially Hermitian then for almost all unitary matrices U ∈ Mc(ℂ), each entry of U* AU is not in S. Some other results of this type are obtained. The ideas here are mainly from differential topology.

KW - Complex matrices

KW - Real analytic map

KW - Unitary orbit

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DO - 10.1137/S0895479800381598

M3 - 文章

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IS - 2

ER -

On the unitary orbit of complex matrices

Abstract

Keywords

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