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On some open questions concerning determinantal inequalities.
- Source :
-
Linear Algebra & its Applications . Jul2020, Vol. 596, p169-183. 15p. - Publication Year :
- 2020
-
Abstract
- In 2017, M. Lin formulated two conjectures concerning determinantal inequalities for positive semi-definite matrices A and B , and which can be stated as follows det (A 2 + | A B | p) ≥ det (A 2 + | B A | p) for p ≥ 0 and det (A 2 + | A B | p) ≥ det (A 2 + A p B p) for 0 ≤ p ≤ 2. The main goal of this paper is to confirm the first conjecture in a slightly more general setting namely in the case when A and B are Hermitian, and also to prove the second conjecture when 0 ≤ p ≤ 4 3. Various related inequalities are then presented and we conclude with an open log-majorization question. [ABSTRACT FROM AUTHOR]
- Subjects :
- *OPEN-ended questions
*MATHEMATICAL equivalence
Subjects
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 596
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 142476518
- Full Text :
- https://doi.org/10.1016/j.laa.2020.03.009