Small Rank Perturbations of H-Expansive Matrices

G. J. Groenewald; D. B. Janse van Rensburg; A. C.M. Ran

doi:10.1007/978-3-031-50613-0_8

Small Rank Perturbations of H-Expansive Matrices

G. J. Groenewald, D. B. Janse van Rensburg, A. C.M. Ran^*

^*Corresponding author for this work

Mathematics

Research output: Chapter in Book / Report / Conference proceeding › Chapter › Academic › peer-review

3 Downloads (Pure)

Abstract

In this paper small rank perturbations of H-expansive and H-unitary matrices are explored. Particular attention is given to the location of eigenvalues with respect to the unit circle for these classes of matrices. The canonical form (in the H-unitary case) and the simple form (in the H-expansive case) for the pair (A,H) will be the starting point.

Original language	English
Title of host publication	Operator and Matrix Theory, Function Spaces, and Applications
Subtitle of host publication	International Workshop on Operator Theory and its Applications 2022, Kraków, Poland [Proceedings]
Editors	Marek Ptak, Hugo J. Woerdeman, Michał Wojtylak
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	203-222
Number of pages	20
ISBN (Electronic)	9783031506130
ISBN (Print)	9783031506123, 9783031506154
DOIs	https://doi.org/10.1007/978-3-031-50613-0_8
Publication status	Published - 2024

Publication series

Name	Operator Theory: Advances and Applications
Volume	295
ISSN (Print)	0255-0156
ISSN (Electronic)	2296-4878

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

Keywords

15A18
15A63
47A55
47B50
Canonical form
H-expansive matrices
H-unitary matrices
Perturbation

Access to Document

10.1007/978-3-031-50613-0_8

Small Rank Perturbations of H-Expansive MatricesFinal published version, 600 KBLicence: Article 25fa Dutch Copyright Act

Persistent URL (handle)

Persistent link

Cite this

Groenewald, G. J., Janse van Rensburg, D. B., & Ran, A. C. M. (2024). Small Rank Perturbations of H-Expansive Matrices. In M. Ptak, H. J. Woerdeman, & M. Wojtylak (Eds.), Operator and Matrix Theory, Function Spaces, and Applications: International Workshop on Operator Theory and its Applications 2022, Kraków, Poland [Proceedings] (pp. 203-222). (Operator Theory: Advances and Applications; Vol. 295). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-50613-0_8

Groenewald, G. J. ; Janse van Rensburg, D. B. ; Ran, A. C.M. / Small Rank Perturbations of H-Expansive Matrices. Operator and Matrix Theory, Function Spaces, and Applications: International Workshop on Operator Theory and its Applications 2022, Kraków, Poland [Proceedings]. editor / Marek Ptak ; Hugo J. Woerdeman ; Michał Wojtylak. Springer Science and Business Media Deutschland GmbH, 2024. pp. 203-222 (Operator Theory: Advances and Applications).

@inbook{63eba7e394534ce6a2776dac97f1d564,

title = "Small Rank Perturbations of H-Expansive Matrices",

abstract = "In this paper small rank perturbations of H-expansive and H-unitary matrices are explored. Particular attention is given to the location of eigenvalues with respect to the unit circle for these classes of matrices. The canonical form (in the H-unitary case) and the simple form (in the H-expansive case) for the pair (A,H) will be the starting point.",

keywords = "15A18, 15A63, 47A55, 47B50, Canonical form, H-expansive matrices, H-unitary matrices, Perturbation",

author = "Groenewald, {G. J.} and {Janse van Rensburg}, {D. B.} and Ran, {A. C.M.}",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.",

year = "2024",

doi = "10.1007/978-3-031-50613-0_8",

language = "English",

isbn = "9783031506123",

series = "Operator Theory: Advances and Applications",

publisher = "Springer Science and Business Media Deutschland GmbH",

pages = "203--222",

editor = "Marek Ptak and Woerdeman, {Hugo J.} and Micha{\l} Wojtylak",

booktitle = "Operator and Matrix Theory, Function Spaces, and Applications",

address = "Germany",

}

Groenewald, GJ, Janse van Rensburg, DB & Ran, ACM 2024, Small Rank Perturbations of H-Expansive Matrices. in M Ptak, HJ Woerdeman & M Wojtylak (eds), Operator and Matrix Theory, Function Spaces, and Applications: International Workshop on Operator Theory and its Applications 2022, Kraków, Poland [Proceedings]. Operator Theory: Advances and Applications, vol. 295, Springer Science and Business Media Deutschland GmbH, pp. 203-222. https://doi.org/10.1007/978-3-031-50613-0_8

Small Rank Perturbations of H-Expansive Matrices. / Groenewald, G. J.; Janse van Rensburg, D. B.; Ran, A. C.M.
Operator and Matrix Theory, Function Spaces, and Applications: International Workshop on Operator Theory and its Applications 2022, Kraków, Poland [Proceedings]. ed. / Marek Ptak; Hugo J. Woerdeman; Michał Wojtylak. Springer Science and Business Media Deutschland GmbH, 2024. p. 203-222 (Operator Theory: Advances and Applications; Vol. 295).

Research output: Chapter in Book / Report / Conference proceeding › Chapter › Academic › peer-review

TY - CHAP

T1 - Small Rank Perturbations of H-Expansive Matrices

AU - Groenewald, G. J.

AU - Janse van Rensburg, D. B.

AU - Ran, A. C.M.

N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

PY - 2024

Y1 - 2024

N2 - In this paper small rank perturbations of H-expansive and H-unitary matrices are explored. Particular attention is given to the location of eigenvalues with respect to the unit circle for these classes of matrices. The canonical form (in the H-unitary case) and the simple form (in the H-expansive case) for the pair (A,H) will be the starting point.

AB - In this paper small rank perturbations of H-expansive and H-unitary matrices are explored. Particular attention is given to the location of eigenvalues with respect to the unit circle for these classes of matrices. The canonical form (in the H-unitary case) and the simple form (in the H-expansive case) for the pair (A,H) will be the starting point.

KW - 15A18

KW - 15A63

KW - 47A55

KW - 47B50

KW - Canonical form

KW - H-expansive matrices

KW - H-unitary matrices

KW - Perturbation

UR - http://www.scopus.com/inward/record.url?scp=85191319494&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85191319494&partnerID=8YFLogxK

U2 - 10.1007/978-3-031-50613-0_8

DO - 10.1007/978-3-031-50613-0_8

M3 - Chapter

AN - SCOPUS:85191319494

SN - 9783031506123

SN - 9783031506154

T3 - Operator Theory: Advances and Applications

SP - 203

EP - 222

BT - Operator and Matrix Theory, Function Spaces, and Applications

A2 - Ptak, Marek

A2 - Woerdeman, Hugo J.

A2 - Wojtylak, Michał

PB - Springer Science and Business Media Deutschland GmbH

ER -

Groenewald GJ, Janse van Rensburg DB, Ran ACM. Small Rank Perturbations of H-Expansive Matrices. In Ptak M, Woerdeman HJ, Wojtylak M, editors, Operator and Matrix Theory, Function Spaces, and Applications: International Workshop on Operator Theory and its Applications 2022, Kraków, Poland [Proceedings]. Springer Science and Business Media Deutschland GmbH. 2024. p. 203-222. (Operator Theory: Advances and Applications). Epub 2024 Apr 3. doi: 10.1007/978-3-031-50613-0_8

Small Rank Perturbations of H-Expansive Matrices

Abstract

Publication series

Bibliographical note

Keywords

Access to Document

Persistent URL (handle)

Other files and links

Fingerprint

Cite this