In this paper, we first give an alternative proof for a result of Mao in [Linear Algebra Appl., 589 (2020) 96–102], then we present some results involving multiple positive definite matrices and multiple sector matrices.
Citation: Sheng Dong, Qingwen Wang, Ming Zhao, Zhiqiang Li. Some results involving multiple matrices[J]. AIMS Mathematics, 2021, 6(11): 12104-12113. doi: 10.3934/math.2021702
In this paper, we first give an alternative proof for a result of Mao in [Linear Algebra Appl., 589 (2020) 96–102], then we present some results involving multiple positive definite matrices and multiple sector matrices.
[1] | W. Berndt, S. Sra, Hlawka-Popoviciu inequalities on positive definite tensors, Linear Algebra Appl., 486 (2015), 317–327. doi: 10.1016/j.laa.2015.08.028 |
[2] | S. Dong, Q. Wang, More generalizations of Hartfiel's inequality and the Brunn-Minkowski inequality, B. Iran. Math. Soc., 47 (2021), 21–29. doi: 10.1007/s41980-020-00363-z |
[3] | X. Fu, Y. Liu, Rotfel'd inequality for partitioned matrices with numerical ranges in a sector, Linear Multilinear Algebra, 64 (2016), 105–109. doi: 10.1080/03081087.2015.1080212 |
[4] | E. V. Haynsworth, Applications of an inequality for the Schur complement, P. Am. Math. Soc., 24 (1970), 512–516. doi: 10.1090/S0002-9939-1970-0255580-7 |
[5] | D. J. Hartfiel, An extension of Haynsworth's determinant inequality, P. Am. Math. Soc., 41 (1973), 463–465. |
[6] | R. A. Horn, C. R. Johnson, Matrix analysis, 2 Eds., Cambridge: Cambridge University Press, 2013. |
[7] | L. Hou, S. Dong, An Extension of Hartfiel's determinant inequality, Math. Inequal. Appl., 21 (2018), 1105–1110. |
[8] | A. George, Kh. D. Ikramov, On the properties of Accretive-Dissipative Matrices, Math. Notes, 77 (2005), 767–776. doi: 10.1007/s11006-005-0077-0 |
[9] | Q. Li, Q. Wang, S. Dong, Extending a result of Haynsworth, J. Math. Inequal., 14 (2020), 845–852. |
[10] | M. Lin, Fischer type determinantal inequalities for accretive-dissipative matrices, Linear Algebra Appl., 438 (2013), 2808–2812. doi: 10.1016/j.laa.2012.11.016 |
[11] | M. Lin, A determinantal inequality for positive definite matrices, Electron J. Linear Algebra, 27 (2014), 821–826. |
[12] | M. Lin, Some inequalities for sector matrices, Oper. Matrices, 10 (2016), 915–921. |
[13] | S. Drury, M. Lin, Singular value inequalities for matrices with numerical ranges in a sector, Oper. Matrices, 8 (2014), 1143–1148. |
[14] | M. Lin, Extension of a result of Hanynsworth and Hartfiel, Arch. Math., 1 (2015), 93–100. |
[15] | M. Lin, D. Zhou, Norm inequalities for accretive-dissipative operator matrices, J. Math. Anal. Appl., 407 (2013), 436–442. doi: 10.1016/j.jmaa.2013.05.042 |
[16] | Y. Mao, Extensions of Hartfiel's inequality to multiple matrices, Linear Algebra Appl., 589 (2020), 96–102. doi: 10.1016/j.laa.2019.12.019 |
[17] | Y. Zheng, X. Jiang, X. Chen, F. Alsaadi, More extensions of a determinant inequality of Hartfiel, Appl. Math. Comput., 369 (2020), 124827. |