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arXiv · 1702.07488

Some inequalities of matrix power and Karcher means for positive linear maps

Rahmatollah Lashkaripour·Monire Hajmohamadi·Mojtaba Bakherad
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Abstract

In this paper, we generalize some matrix inequalities involving matrix power and Karcher means of positive definite matrices. Among other inequalities, it is shown that if ${\mathbb A}=(A_{1},...,A_{n})$ is a $n$-tuple of positive definite matrices such that $0 0$, $\alpha=\max\Big\{\frac{(M+m)^{2}}{4Mm}, \frac{(M+m)^{2}}{4^{\frac{2}{p}}Mm}\Big\}$, $\Phi$ is a positive unital linear map and $t\in [-1, 1]\backslash \{0\}$.

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Rahmatollah Lashkaripour, Monire Hajmohamadi, Mojtaba Bakherad. 2017-02-24. Some inequalities of matrix power and Karcher means for positive linear maps. https://arxiv.org/abs/1702.07488

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