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Mat. Zametki, 2005, Volume 77, Issue 6, Pages 832–843 (Mi mz2542)  

This article is cited in 21 scientific papers (total in 21 papers)

On the Properties of Accretive-Dissipative Matrices

A. Georgea, Kh. D. Ikramovb

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

Abstract: Let $A$ be a complex $(n\times n)$ matrix, and let $A=B+iC$, $B=B^*$, $C=C^*$ be its Toeplitz decomposition. Then $A$ is said to be (strictly) accretive if $B>0$ and (strictly) dissipative if $C>0$. 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.

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

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English version:
Mathematical Notes, 2005, 77:6, 767–776

Bibliographic databases:

UDC: 512
Received: 03.02.2004
Revised: 13.09.2004

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
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Mao Ya., Liu X., “On Some Inequalities For Accretive-Dissipative Matrices”, Linear Multilinear Algebra  crossref  isi
    2. Kh. D. Ikramov, “Gaussian elimination and the ranks of the components in the Cartesian decomposition of a matrix”, J. Math. Sci. (N. Y.), 157:5 (2009), 689–691  mathnet  crossref  zmath
    3. Kh. D. Ikramov, “The inertia of the components in the cartesian decomposition of a square matrix”, Dokl. Math., 78:1 (2008), 601–603  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    4. Kh. D. Ikramov, “On complex Benzi-Golub matrices”, Dokl. Math., 79:3 (2009), 342–344  mathnet  crossref  mathscinet  zmath  zmath  isi  elib  elib  scopus
    5. Kh. D. Ikramov, “Subdirect sums and differences for some classes of matrices”, Comput. Math. Math. Phys., 50:1 (2010), 7–11  mathnet  crossref  mathscinet  adsnasa  isi
    6. Lin M., “Reversed Determinantal Inequalities for Accretive-Dissipative Matrices”, Math. Inequal. Appl., 15:4 (2012), 955–958  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    7. Lin M., “Fischer Type Determinantal Inequalities for Accretive-Dissipative Matrices”, Linear Alg. Appl., 438:6 (2013), 2808–2812  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    8. Lin M., Zhou D., “Norm Inequalities for Accretive-Dissipative Operator Matrices”, J. Math. Anal. Appl., 407:2 (2013), 436–442  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    9. Fu X., He Ch., “On Some Fischer-Type Determinantal Inequalities for Accretive-Dissipative Matrices”, J. Inequal. Appl., 2013, 316  crossref  mathscinet  isi  scopus  scopus
    10. Yang J., “Some Determinantal Inequalities for Accretive-Dissipative Matrices”, J. Inequal. Appl., 2013, 512  crossref  mathscinet  zmath  isi  scopus  scopus
    11. Zhang Yu., “Unitarily Invariant Norm Inequalities for Accretive-Dissipative Operator Matrices”, J. Math. Anal. Appl., 412:1 (2014), 564–569  crossref  mathscinet  zmath  isi  scopus  scopus
    12. Drury S., Lin M., “Reversed Fischer Determinantal Inequalities”, Linear Multilinear Algebra, 62:8 (2014), 1069–1075  crossref  mathscinet  zmath  isi  scopus  scopus
    13. Lin M., “Extension of a Result of Haynsworth and Hartfiel”, Arch. Math., 104:1 (2015), 93–100  crossref  mathscinet  zmath  isi  scopus
    14. Drury S., “Principal Powers of Matrices With Positive Definite Real Part”, Linear Multilinear Algebra, 63:2 (2015), 296–301  crossref  mathscinet  zmath  isi  scopus  scopus
    15. Xue J., Hu X., “on Fischer-Type Determinantal Inequalities For Accretive-Dissipative Matrices”, J. Inequal. Appl., 2015, 194  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    16. Liu J., “Generalizations of the Brunn?Minkowski inequality”, Linear Alg. Appl., 508 (2016), 206–213  crossref  mathscinet  zmath  isi  elib  scopus
    17. Zhang D., Hou L., Ma L., “Properties of Matrices With Numerical Ranges in a Sector”, Bull. Iran Math. Soc., 43:6 (2017), 1699–1707  mathscinet  isi
    18. 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  crossref  mathscinet  isi  scopus
    19. Hou L., Zhang D., “Concave Functions of Partitioned Matrices With Numerical Ranges in a Sector”, Math. Inequal. Appl., 20:2 (2017), 583–589  crossref  mathscinet  zmath  isi  scopus  scopus
    20. Dong Sh., Hou L., “A Complement of the Hadamard-Fischer Inequality”, J. Intell. Fuzzy Syst., 35:4 (2018), 4011–4015  crossref  isi  scopus
    21. Hou L., Dong Sh., “An Extension of Hartfiel'S Determinant Inequality”, Math. Inequal. Appl., 21:4 (2018), 1105–1110  crossref  mathscinet  zmath  isi  scopus
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