Some determinantal inequalities for Hadamard and Fan products of matrices

Abstract

In this note, we generalize some determinantal inequalities which are due to Lynn (Proc. Camb.

An Oppenheim type determinantal inequality for the Khatri-Rao product

“…In the sequel, by setting q 1 = q 2 = • • • = q m = 1 in Theorem 2.5 and Theorem 2.6, we can get the following Corollary 2.7 and Corollary 2.8 for the Hadamard product, respectively. These two corollaries are extensions of Oppenheim-Schur's inequality (4) and Chen's result (5). The first corollary can be found in [5,Theorem 7] and the second one can be seen in [4,Theorem 4].…”

“…These two corollaries are extensions of Oppenheim-Schur's inequality (4) and Chen's result (5). The first corollary can be found in [5,Theorem 7] and the second one can be seen in [4,Theorem 4]. µµ .…”

“…We first modify Kim's result (6) to more general setting where the blocks in each n × n block matrix are of different order. Motivated by the works in [5] and [4], we then show extensions of our results to multiple block positive semidefinite matrices. Our results extend the above mentioned results (4), ( 5) and ( 6).…”

An Oppenheim type inequality for positive definite block matrices

“…Over the years, various generalizations and extensions of (4) and ( 5) have been obtained in the literature. For instance, see [23,24] for the equality cases; see [2,15,22,4,7] for the extensions of M -matrices. It is worth noting that Lin [16] recently gave a remarkable extension (Theorem 1.1) of Chen's result (5) for positive definite block matrices.…”