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

Hosoo Lee; Yongdo Lim

doi:10.1007/s00013-006-1934-0

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

Hosoo Lee
, Yongdo Lim

Kyungpook National University

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we prove that the inverse mean problem of geometric and golden means of positive definite matrices { A = X#Y B = 1/2(X + X#(4Y - 3X)) is solvable (resp. uniquely solvable) if and only if A ≤ √3B ≤ 2A (resp. A ≤ √3B ≤ √3A).

Original language	English
Pages (from-to)	90-95
Number of pages	6
Journal	Archiv der Mathematik
Volume	88
Issue number	1
DOIs	https://doi.org/10.1007/s00013-006-1934-0
State	Published - Jan 2007
Externally published	Yes

Keywords

Geometric means
Golden mean
Inverse problem
Nonlinear matrix equation
Positive definite matrix

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10.1007/s00013-006-1934-0

Cite this

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title = "The inverse problem of geometric and golden means of positive definite matrices",

abstract = "In this paper we prove that the inverse mean problem of geometric and golden means of positive definite matrices \{ A = X\#Y B = 1/2(X + X\#(4Y - 3X)) is solvable (resp. uniquely solvable) if and only if A ≤ √3B ≤ 2A (resp. A ≤ √3B ≤ √3A).",

keywords = "Geometric means, Golden mean, Inverse problem, Nonlinear matrix equation, Positive definite matrix",

author = "Hosoo Lee and Yongdo Lim",

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AB - In this paper we prove that the inverse mean problem of geometric and golden means of positive definite matrices { A = X#Y B = 1/2(X + X#(4Y - 3X)) is solvable (resp. uniquely solvable) if and only if A ≤ √3B ≤ 2A (resp. A ≤ √3B ≤ √3A).

KW - Geometric means

KW - Golden mean

KW - Inverse problem

KW - Nonlinear matrix equation

KW - Positive definite matrix

UR - https://www.scopus.com/pages/publications/33847001612

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DO - 10.1007/s00013-006-1934-0

M3 - Article

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JF - Archiv der Mathematik

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

Abstract

Keywords

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