Abstract

DRAGOMIR, SILVESTRU SEVER. Determinant Inequalities for Positive Definite Matrices Via Additive and Multiplicative Young Inequalities. Integración - UIS [online]. 2022, vol.40, n.2, pp.193-206.  Epub May 08, 2023. ISSN 0120-419X.  https://doi.org/10.18273/revint.v40n2-2022004.

In this paper we prove among others that, if the positive definite matrices A, B of order n satisfy the condition 0 < mIn ≤ B − A ≤ M In, for some constants 0 < m < M, where In is the identity matrix, then 0 ≤ (1 − t) [det (A)]−1 + t [det (A + mIn)]−1 − [det (A + mtIn)]−1 ≤ (1 − t) [det (A)]−1 + t [det (B)]−1 − [det ((1 − t) A + tB)]−1 ≤ (1 − t) [det (A)]−1 + t [det (A + M In)]−1 − [det (A + M tIn)]−1 , for all t ∈ [0, 1] .

Keywords : Positive definite matrices; Determinants; Inequalities.

        · abstract in Spanish     · text in English     · English ( pdf )