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Revista Integración
versión impresa ISSN 0120-419Xversión On-line ISSN 2145-8472
Resumen
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 08-Mayo-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] .
MSC2010:
47A63, 26D15, 46C05.
Palabras clave : Positive definite matrices; Determinants; Inequalities.