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

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

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

Keywords

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

All Science Journal Classification (ASJC) codes

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2019.01.029

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

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.",

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

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

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2019",

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

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T1 - More on geometry of Krein space C-numerical range

AU - Guterman, Alexander

AU - Lemos, Rute

AU - Soares, Graça

PY - 2019/7/1

Y1 - 2019/7/1

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

UR - http://www.scopus.com/inward/record.url?scp=85061708371&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2019.01.029

DO - 10.1016/j.amc.2019.01.029

M3 - مقالة

SN - 0096-3003

VL - 352

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

Keywords

All Science Journal Classification (ASJC) codes

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