On the symmetric matrix word equation XBX2B3X 2BX = A

Yongdo Lim

doi:10.1016/j.laa.2007.06.021

On the symmetric matrix word equation XBX²B³X ²BX = A

Yongdo Lim

Kyungpook National University

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

Abstract

In this paper we present explicitly the unique positive definite solution of the symmetric word equation XBX²B³X²BX = A over 2×2 positive definite matrices. This word equation appeared as a counterexample to the uniqueness of solution conjecture for symmetric word equations; it has multiple positive definite solutions for certain 3x3 positive definite matrices A and. B.

Original language	English
Pages (from-to)	77-86
Number of pages	10
Journal	Linear Algebra and Its Applications
Volume	427
Issue number	1
DOIs	https://doi.org/10.1016/j.laa.2007.06.021
State	Published - 1 Nov 2007
Externally published	Yes

Keywords

Geometric mean
Positive definite matrix
Symmetric word equation

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10.1016/j.laa.2007.06.021

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title = "On the symmetric matrix word equation XBX2B3X 2BX = A",

abstract = "In this paper we present explicitly the unique positive definite solution of the symmetric word equation XBX2B3X2BX = A over 2×2 positive definite matrices. This word equation appeared as a counterexample to the uniqueness of solution conjecture for symmetric word equations; it has multiple positive definite solutions for certain 3x3 positive definite matrices A and. B.",

keywords = "Geometric mean, Positive definite matrix, Symmetric word equation",

author = "Yongdo Lim",

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doi = "10.1016/j.laa.2007.06.021",

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AU - Lim, Yongdo

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N2 - In this paper we present explicitly the unique positive definite solution of the symmetric word equation XBX2B3X2BX = A over 2×2 positive definite matrices. This word equation appeared as a counterexample to the uniqueness of solution conjecture for symmetric word equations; it has multiple positive definite solutions for certain 3x3 positive definite matrices A and. B.

AB - In this paper we present explicitly the unique positive definite solution of the symmetric word equation XBX2B3X2BX = A over 2×2 positive definite matrices. This word equation appeared as a counterexample to the uniqueness of solution conjecture for symmetric word equations; it has multiple positive definite solutions for certain 3x3 positive definite matrices A and. B.

KW - Geometric mean

KW - Positive definite matrix

KW - Symmetric word equation

UR - https://www.scopus.com/pages/publications/79954452039

U2 - 10.1016/j.laa.2007.06.021

DO - 10.1016/j.laa.2007.06.021

M3 - Article

AN - SCOPUS:79954452039

SN - 0024-3795

VL - 427

SP - 77

EP - 86

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1

ER -

On the symmetric matrix word equation XBX²B³X ²BX = A

Abstract

Keywords

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