Research article

Inequalities on $ 2\times 2 $ block accretive partial transpose matrices

  • Received: 27 December 2023 Revised: 04 February 2024 Accepted: 20 February 2024 Published: 01 March 2024
  • MSC : 15A18, 15A42, 15A45, 15A60

  • In this note, we first corrected a result of Alakhrass [1], then presented some inequalities related to $ 2\times 2 $ block accretive partial transpose matrices which generalized some results on block positive partial transpose matrices.

    Citation: Lihong Hu, Junjian Yang. Inequalities on $ 2\times 2 $ block accretive partial transpose matrices[J]. AIMS Mathematics, 2024, 9(4): 8805-8813. doi: 10.3934/math.2024428

    Related Papers:

  • In this note, we first corrected a result of Alakhrass [1], then presented some inequalities related to $ 2\times 2 $ block accretive partial transpose matrices which generalized some results on block positive partial transpose matrices.



    加载中


    [1] M. Alakhrass, A note on positive partial transpose blocks, AIMS Mathematics, 8 (2023), 23747–23755. https://doi.org/10.3934/math.20231208 doi: 10.3934/math.20231208
    [2] R. Bhatia, Matrix analysis, New York: Springer, 1997. https://doi.org/10.1007/978-1-4612-0653-8
    [3] R. Bhatia, Positive definite matrices, Princeton: Princeton University Press, 2007.
    [4] R. Bhatia, P. Grover, Norm inequalities related to the matrix geometric mean, Linear Algebra Appl., 437 (2012), 726–733. https://doi.org/10.1016/j.laa.2012.03.001 doi: 10.1016/j.laa.2012.03.001
    [5] X. Fu, P. S. Lau, T. Y. Tam, Inequalities on $2\times 2$ block positive semidefinite matrices, Linear Multilinear A., 70 (2022), 6820–6829. https://doi.org/10.1080/03081087.2021.1969327 doi: 10.1080/03081087.2021.1969327
    [6] X. Fu, L. Hu, S. A. Haseeb, Inequalities for partial determinants of accretive block matrices, J. Inequal. Appl., 2023 (2023), 101. https://doi.org/10.1186/s13660-023-03008-x doi: 10.1186/s13660-023-03008-x
    [7] S. Hayat, J. H. Koolen, F. Liu, Z. Qiao, A note on graphs with exactly two main eigenvalues, Linear Algebra Appl., 511 (2016), 318–327. https://doi.org/10.1016/j.laa.2016.09.019 doi: 10.1016/j.laa.2016.09.019
    [8] S. Hayat, M. Javaid, J. H. Koolen, Graphs with two main and two plain eigenvalues, Appl. Anal. Discr. Math., 11 (2017), 244–257. https://doi.org/10.2298/AADM1702244H doi: 10.2298/AADM1702244H
    [9] J. H. Koolen, S. Hayat, Q. Iqbal, Hypercubes are determined by their distance spectra, Linear Algebra Appl., 505 (2016), 97–108. https://doi.org/10.1016/j.laa.2016.04.036 doi: 10.1016/j.laa.2016.04.036
    [10] L. Kuai, An extension of the Fiedler-Markham determinant inequality, Linear Multilinear A., 66 (2018), 547–553. https://doi.org/10.1080/03081087.2017.1304521 doi: 10.1080/03081087.2017.1304521
    [11] E. Y. Lee, The off-diagonal block of a PPT matrix, Linear Algebra Appl., 486 (2015), 449–453. https://doi.org/10.1016/j.laa.2015.08.018 doi: 10.1016/j.laa.2015.08.018
    [12] M. Lin, Inequalities related to $2\times 2$ block PPT matrices, Oper. Matrices, 9 (2015), 917–924. http://doi.org/10.7153/oam-09-54 doi: 10.7153/oam-09-54
    [13] H. Xu, X. Fu, S. A. Haseeb, Trace inequalities related to $2 \times 2$ block sector matrices, Oper. Matrices, 17 (2023), 367–374. http://doi.org/10.7153/oam-2023-17-26 doi: 10.7153/oam-2023-17-26
  • Reader Comments
  • © 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(564) PDF downloads(54) Cited by(0)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog