determinantal inequality
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2021 ◽  
Vol 87 (3) ◽  
pp. 673-682
Author(s):  
Amir Hossein Ghodrati ◽  

We use Hadamard's determinantal inequality and its generalization to prove some upper bounds on the energy of a graph in terms of degrees, average 2-degrees and number of common neighbors of its vertices. Also, we prove an inequality relating the energy of a graph and one arbitrary subgraph of it.


2020 ◽  
Vol 605 ◽  
pp. 21-28
Author(s):  
Mohammad M. Ghabries ◽  
Hassane Abbas ◽  
Bassam Mourad ◽  
Abdallah Assi

2017 ◽  
Vol 65 (10) ◽  
pp. 2024-2030 ◽  
Author(s):  
Minghua Lin ◽  
Fuzhen Zhang

2016 ◽  
Vol 59 (3) ◽  
pp. 585-591 ◽  
Author(s):  
Minghua Lin

AbstractLet A be a density matrix in . Audenaert [J. Math. Phys. 48(2007) 083507] proved an inequality for Schatten p-norms:where Tr1 and Tr2 stand for the first and second partial trace, respectively. As an analogue of his result, we prove a determinantal inequality


2016 ◽  
Vol 19 (05) ◽  
pp. 1650044 ◽  
Author(s):  
Minghua Lin

In comparing geodesics induced by different metrics, Audenaert formulated the following determinantal inequality [Formula: see text] where [Formula: see text] are [Formula: see text] positive semidefinite matrices. We complement his result by proving [Formula: see text] Our proofs feature the fruitful interplay between determinantal inequalities and majorization relations. Some related questions are mentioned.


2016 ◽  
Vol 99 (1-2) ◽  
pp. 164-165 ◽  
Author(s):  
Minghua Lin ◽  
Suvrit Sra

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