Some applications of a majorization inequality due to Bapat and Sunder. (English) Zbl 1310.15033

Summary: This paper presents applications of a remarkable majorization inequality due to R. B. Bapat and V. S. Sunder [Linear Algebra Appl. 72, 107–117 (1985; Zbl 0577.15016)] in three different areas. The first application is a proof of T. Hiroshima’s result [“Majorization criterion for distillability of a bipartite quantum state”, Phys. Rev. Lett. 91, No. 5, Article ID 057902 (2003; doi:10.1103/PhysRevLett.91.057902)] which arises in quantum information theory. The second one is an extension of some eigenvalue inequalities that have been used to bound chromatic number of graphs. The third application is a simplified proof of a majorization inequality from the analysis of distributed Kalman filtering.


15A45 Miscellaneous inequalities involving matrices


Zbl 0577.15016
Full Text: DOI


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