New determinantal inequalities concerning Hermitian and positive semi-definite matrices

Abbas, Hassan; Ghabries, Mohammad M.; Mourad, Bassam

doi:10.7153/oam-2021-15-07

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Remark 31 Motivated By Theorem 31 One Naturally Would Ask Wh...1

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“…Our next goal is to show a result that strengthens Conjecture 1.1. For this, we need the following lemma whose proof can be found in [2]. Lemma 3.2 Let A be a positive semi-definite matrix and B be a Hermitian matrix.…”

Section: Remark 31 Motivated By Theorem 31 One Naturally Would Ask Wh...mentioning

confidence: 99%

New log-majorization results concerning eigenvalues and singular values and a complement of a norm inequality

Ghabries¹,

Abbas²,

Mourad³

et al. 2021

Preprint

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The purpose of this paper is to establish new log-majorization results concerning eigenvalues and singular values which generalize some previous work related to a conjecture and an open question which were presented by R. Lemos and G. Soares in [11]. In addition, we present a complement of a unitarily invariant norm inequality which was conjectured by R. Bhatia, Y. Lim and T. Yamazaki in [4], and recently proved by T.H. Dinh, R. Dumitru and J.A. Franco in [5] for the Schatten p-norm with 1 ≤ p ≤ ∞.

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Section: Remark 31 Motivated By Theorem 31 One Naturally Would Ask Wh...mentioning

confidence: 99%

New log-majorization results concerning eigenvalues and singular values and a complement of a norm inequality

Ghabries¹,

Abbas²,

Mourad³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

New log-majorization results concerning eigenvalues and singular values and a complement of a norm inequality

Ghabries

Abbas

Mourad

et al. 2022

Linear and Multilinear Algebra

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New determinantal inequalities concerning Hermitian and positive semi-definite matrices

Abstract: Let A,B be n × n matrices such that A is positive semi-definite and B is Hermitian. In this note, it is shown, among other inequalities, the following determinantal inequality

Cited by 2 publications

References 0 publications

New log-majorization results concerning eigenvalues and singular values and a complement of a norm inequality

New log-majorization results concerning eigenvalues and singular values and a complement of a norm inequality

New log-majorization results concerning eigenvalues and singular values and a complement of a norm inequality

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