The inverse problem of geometric and golden means of positive definite matrices期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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The inverse problem of geometric and golden means of positive definite matrices

Authors:

Hosoo Lee Yongdo Lim

Institution:

(1) Department of Mathematics, Kyungpook National University, Taegu, 702-701, Korea

Abstract:

In this paper we prove that the inverse mean problem of geometric and golden means of positive definite matrices

$\left\{ \begin{aligned} & A = X\# Y\\ & B = \frac{1} {2}(X+X\# (4Y - 3X)) \end{aligned} \right.$

is solvable (resp. uniquely solvable) if and only if $A \leq{\sqrt {3}B} \leq 2A({\text{resp}}. A \leq {\sqrt {3}B} \leq{\sqrt {3}A})$ . Received: 9 March 2006

Keywords:

Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 15A24 15A29 15A48

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