A. George, Kh. D. Ikramov, “On the Properties of Accretive-Dissipative Matrices”, Mat. Zametki, 77:6 (2005), 832–843; Math. Notes, 77:6 (2005), 767

Matematicheskie Zametki

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Forthcoming papers
	Archive
	Impact factor
	Guidelines for authors
	License agreement
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Mat. Zametki:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Matematicheskie Zametki, 2005, Volume 77, Issue 6, Pages 832–843
DOI: https://doi.org/10.4213/mzm2542 (Mi mzm2542)

This article is cited in 36 scientific papers (total in 36 papers)

On the Properties of Accretive-Dissipative Matrices

A. George^a, Kh. D. Ikramov^b

^a University of Waterloo
^b M. V. Lomonosov Moscow State University

Full-text PDF (218 kB) Citations (36)

References:

PDF

HTML

DOI: https://doi.org/10.4213/mzm2542

Abstract: Let

A

$A$ be a complex

(n \times n)

$(n\times n)$ matrix, and let

A = B + i C

$A=B+iC$ ,

B = B^{*}

$B=B^*$ ,

C = C^{*}

$C=C^*$ be its Toeplitz decomposition. Then

A

$A$ is said to be (strictly) accretive if

B > 0

$B>0$ and (strictly) dissipative if

C > 0

$C>0$ . We study the properties of matrices that satisfy both these conditions, in other words, of accretive-dissipative matrices. In many respects, these matrices behave as numbers in the first quadrant of the complex plane. Some other properties are natural extensions of the corresponding properties of Hermitian positive-definite matrices.

Received: 03.02.2004
Revised: 13.09.2004

English version:
Mathematical Notes, 2005, Volume 77, Issue 6, Pages 767–776
DOI: https://doi.org/10.1007/s11006-005-0077-0

Bibliographic databases:

UDC: 512

Language: Russian

Citation: A. George, Kh. D. Ikramov, “On the Properties of Accretive-Dissipative Matrices”, Mat. Zametki, 77:6 (2005), 832–843; Math. Notes, 77:6 (2005), 767–776

Citation in format AMSBIB

\Bibitem{GeoIkr05}

\by A.~George, Kh.~D.~Ikramov

\paper On the Properties of Accretive-Dissipative Matrices

\jour Mat. Zametki

\yr 2005

\vol 77

\issue 6

\pages 832--843

\mathnet{http://mi.mathnet.ru/mzm2542}

\crossref{https://doi.org/10.4213/mzm2542}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2246959}

\zmath{https://zbmath.org/?q=an:1079.15021}

\elib{https://elibrary.ru/item.asp?id=9155832}

\transl

\jour Math. Notes

\yr 2005

\vol 77

\issue 6

\pages 767--776

\crossref{https://doi.org/10.1007/s11006-005-0077-0}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000230336000017}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-21644435377}

Linking options:

https://www.mathnet.ru/eng/mzm2542

https://doi.org/10.4213/mzm2542

https://www.mathnet.ru/eng/mzm/v77/i6/p832

This publication is cited in the following 36 articles:

Yanling Mao, Guoxing Ji, “On Rotfel'd type inequalities for sectorial matrices”, Linear Algebra and its Applications, 691 (2024), 123
Mao Ya., Liu X., “On Some Inequalities For Accretive-Dissipative Matrices”, Linear Multilinear Algebra, 69:9 (2021), 1657–1664
Dong Sh., Wang Q.-W., “More Generalizations of Hartfiel'S Inequality and the Brunn-Minkowski Inequality”, Bull. Iran Math. Soc., 47:1 (2021), 21–29
Bourahli A., Hirzallah O., Kittaneh F., “Unitarily Invariant Norm Inequalities For Functions of Accretive -Dissipative 2 X 2 Block Matrices”, Positivity, 25:2 (2021), 447–467
Lu J., Zhang Ch., “On the Strong P-Regular Splitting Iterative Methods For Non-Hermitian Linear Systems”, AIMS Math., 6:11 (2021), 11879–11893
Dong Sh., Wang Q., Zhao M., Li Zh., “Some Results Involving Multiple Matrices”, AIMS Math., 6:11 (2021), 12104–12113
Alakhrass M., “On Sectorial Matrices and Their Inequalities”, Linear Alg. Appl., 617 (2021), 179–189
Fu X., Lau P.-Sh., Tam T.-Ya., “Norm Inequalities For Sector Block Matrices”, Linear Alg. Appl., 605 (2020), 249–262
Li Q., Wang Q., Dong Sh., “Extending a Result of Haynsworth”, J. Math. Inequal., 14:3 (2020), 845–852
Zhou X., “Norm Inequalities For Submultiplicative Functions Involving Contraction Sector 2 X 2 Block Matrices”, J. Inequal. Appl., 2020:1 (2020), 247
Zheng Ya., Jiang X., Chen X., Alsaadi F., “More Extensions of a Determinant Inequality of Hartfiel”, Appl. Math. Comput., 369 (2020), 124827
Yang J., “A Note on Unitarily Invariant Norm Inequalities For Accretive-Dissipative Operator Matrices”, Ital. J. Pure Appl. Math., 2020, no. 43, 206–212
Wang D., Chen W., Khong S.Zh., Qiu L., “On the Phases of a Complex Matrix”, Linear Alg. Appl., 593 (2020), 152–179
Li Y., Feng L., “Extensions of Brunn-Minkowski'S Inequality to Multiple Matrices”, Linear Alg. Appl., 603 (2020), 91–100
Yongtao Li, Lihua Feng, “Extensions of Brunn-Minkowski's inequality to multiple matrices”, Linear Algebra and its Applications, 603 (2020), 91
Tan F., Xie A., “On the Logarithmic Mean of Accretive Matrices”, Filomat, 33:15 (2019), 4747–4752
Dong Sh., Hou L., “A Complement of the Hadamard-Fischer Inequality”, J. Intell. Fuzzy Syst., 35:4 (2018), 4011–4015
Hou L., Dong Sh., “An Extension of Hartfiel'S Determinant Inequality”, Math. Inequal. Appl., 21:4 (2018), 1105–1110
Zhang D., Hou L., Ma L., “Properties of Matrices With Numerical Ranges in a Sector”, Bull. Iran Math. Soc., 43:6 (2017), 1699–1707
Gumus I.H., Hirzallah O., Kittaneh F., “Norm Inequalities Involving Accretive-Dissipative 2 X 2 Block Matrices”, Linear Alg. Appl., 528:SI (2017), 76–93

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	796
Full-text PDF :	288
References:	112
First page:	1

Что такое QR-код?

Registration to the website

Logotypes