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Drury, S., Lin, M.: Singular value inequalities for matrices with numerical ranges in a sector. Oper. Matrices 8, 1143–1148 (2014)
Fan, K.: Some inequalities concerning positive-definite Hermitian matrices. Proc. Camb. Philos. Soc. 51, 414–421 (1955)
George, A., Ikramov, K.H.D.: On the properties of accretive–dissipative matrices. Math. Notes 77, 767–776 (2005)
Hartfiel, D.J.: An extension of Haynsworth’s determinant inequality. Proc. Amer. Math. Soc. 41, 463–465 (1973)
Haynsworth, E.V.: Applications of an inequality for the Schur complement. Proc. Amer. Math. Soc. 21, 512–516 (1970)
Hou, L., Dong, S.: An extension of Hartfiel’s determinant inequality. Math. Inequal. Appl. 21, 1105–1110 (2018)
Horn, R.A., Johnson, C.R.: Matrix Analysis, 2nd edn. Cambridge University Press, Cambridge (2013)
Ikramov, K.H.D.: Determinantal inequalities for accretive–dissipative matrices. J. Math. Sci. 121, 2458–2464 (2004)
Lin, M.: Fischer type determinantal inequalities for accretive–dissipative matrices. Linear Algebra Appl. 438, 2808–2812 (2013)
Lin, M.: Extension of a result of Hanynsworth and Hartfiel. Arch. Math. 104, 93–100 (2015)
Lin, M.: Some inequalities for sector matrices. Oper. Matrices 10, 915–921 (2016)
Lin, M., Zhou, D.: Norm inequalities for accretive–dissipative operator matrices. J. Math. Anal. Appl. 407, 436–442 (2013)
Liu, J.: Generalizations of the Brunn–Minkowski inequality. Linear Algebra Appl. 508, 206–213 (2016)
Yuan, J., Leng, G.: A generalization of the matrix form of the Brunn–Minkowski inequality. J. Aust. Math. Soc. 83, 125–134 (2007)
Zhang, D., Hou, L., Ma, L.: Properties of matrices with numerical ranges in a sector. Bull. Iran. Math. Soc. 43, 1699–1707 (2017)
Zheng, Y., Jiang, X., Chen, X., Alsaadi, F.: More extensions of a determinant inequality of Hartfiel. Linear Algebra Appl. 369, 124827 (2020)
We acknowledge the helpful comments from the referee. The work was supported by National Natural Science Foundation of China (NNSFC) [Grant number 11971294].
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Communicated by Abbas Salemi.
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Dong, S., Wang, Q. More Generalizations of Hartfiel’s Inequality and the Brunn–Minkowski Inequality. Bull. Iran. Math. Soc. (2020). https://doi.org/10.1007/s41980-020-00363-z
- Hartfiel’s inequality
- The Brunn–Minkowski inequality
- Sector matrices
Mathematics Subject Classification