More on geometry of Krein space C-numerical range

Alexander Guterman; Rute Lemos; Graça Soares

doi:10.1016/j.amc.2019.01.029

More on geometry of Krein space C-numerical range

Alexander Guterman
, Rute Lemos
, Graça Soares

Lomonosov Moscow State University
Moscow Institute of Physics and Technology
University of Aveiro
Universidade de Trás-os-Montes e Alto Douro

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

3 Scopus citations

Abstract

For n × n complex matrices A, C and H, where H is non-singular Hermitian, the Krein space C-numerical range of A induced by H is the subset of the complex plane given by {Tr(CU ^[*] AU):U ⁻¹ =U ^[*] } with U ^[*] =H ⁻¹ U ^* H the H-adjoint matrix of U. We revisit several results on the geometry of Krein space C-numerical range of A and in particular we obtain a condition for the Krein space C-numerical range to be a subset of the real line.

Original language	English
Pages (from-to)	258-269
Number of pages	12
Journal	Applied Mathematics and Computation
Volume	352
DOIs	https://doi.org/10.1016/j.amc.2019.01.029
State	Published - 1 Jul 2019
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2019 Elsevier Inc.

Funding

The work of the first author is supported by the grant RSF 17-11-01124. The work of the second author was supported by Portuguese funds through the Center for Research and Development in Mathematics and Applications (CIDMA) and the Portuguese Foundation for Science and Technology (FCT - Fundação para a Ciência e a Tecnologia) , within the project UID/MAT/0416/2013 . The work of the third author was financed by Portuguese Funds through FCT - Fundação para a Ciência e Tecnologia , within the Project UID/MAT/00013/2013 .

Funders	Funder number
Fundo Regional para a Ciência e Tecnologia
Fundação para a Ciência e a Tecnologia	UID/MAT/0416/2013, UID/MAT/00013/2013
Instituto Nacional de Ciência e Tecnologia para Excitotoxicidade e Neuroproteção
Fundació Catalana de Trasplantament
Center for Research and Development in Mathematics and Applications

Keywords

Indefininte inner product
J−Hermitian matrix
Krein space C-numerical range

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10.1016/j.amc.2019.01.029

Cite this

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title = "More on geometry of Krein space C-numerical range",

abstract = " For n {\texttimes} n complex matrices A, C and H, where H is non-singular Hermitian, the Krein space C-numerical range of A induced by H is the subset of the complex plane given by \{Tr(CU [*] AU):U −1 =U [*] \} with U [*] =H −1 U * H the H-adjoint matrix of U. We revisit several results on the geometry of Krein space C-numerical range of A and in particular we obtain a condition for the Krein space C-numerical range to be a subset of the real line.",

keywords = "Indefininte inner product, J−Hermitian matrix, Krein space C-numerical range",

author = "Alexander Guterman and Rute Lemos and Gra{\c c}a Soares",

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year = "2019",

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doi = "10.1016/j.amc.2019.01.029",

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AU - Lemos, Rute

AU - Soares, Graça

PY - 2019/7/1

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N2 - For n × n complex matrices A, C and H, where H is non-singular Hermitian, the Krein space C-numerical range of A induced by H is the subset of the complex plane given by {Tr(CU [*] AU):U −1 =U [*] } with U [*] =H −1 U * H the H-adjoint matrix of U. We revisit several results on the geometry of Krein space C-numerical range of A and in particular we obtain a condition for the Krein space C-numerical range to be a subset of the real line.

AB - For n × n complex matrices A, C and H, where H is non-singular Hermitian, the Krein space C-numerical range of A induced by H is the subset of the complex plane given by {Tr(CU [*] AU):U −1 =U [*] } with U [*] =H −1 U * H the H-adjoint matrix of U. We revisit several results on the geometry of Krein space C-numerical range of A and in particular we obtain a condition for the Krein space C-numerical range to be a subset of the real line.

KW - Indefininte inner product

KW - J−Hermitian matrix

KW - Krein space C-numerical range

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SN - 0096-3003

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SP - 258

EP - 269

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

More on geometry of Krein space C-numerical range

Abstract

Bibliographical note

Funding

Keywords

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