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Linear and Multilinear Algebra Volume 67, 2019 - Issue 5
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Original Articles

The unique solution of the Karcher equation and the self-adjointness of the Karcher mean

Jun Ichi FujiiDepartment of Arts and Sciences (Information Science), Osaka Kyoiku University, Osaka, Japan.View further author information
&
Yuki SeoDepartment of Mathematics Education, Osaka Kyoiku University, Osaka, Japan.Correspondence[email protected]
View further author information
Pages 976-986 | Received 20 Oct 2017, Accepted 02 Feb 2018, Published online: 15 Feb 2018

References

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  • Fujii JI , Kamei E . Relative operator entropy in noncommutative information theory. Math Japon. 1989;34:341–348.
  • Fujii JI , Seo Y . Tsallis relative operator entropy with negative paramaeters. Adv Oper Theory. 2016;1(2):219–236.
  • Kamei E . Geometrical expansion of an operator equation. Sci Math Jpn. 2017;80:153–160.
  • Fujii JI , Seo Y . The relative operator entropy and the Karcher mean. Linear Algebra Appl. 2018;542:4–34.
  • Yamazaki T . Riemannian mean and matrix inequalities related to the Ando-Hiai inequality and chaotic order. Oper Matrices. 2012;6:577–588.
  • Dehgani M , Kian M , Seo Y . Matrix power means and the information monotonicity. Linear Algebra Appl. 2017;521:57–69.
  • Kubo F , Ando T . Means of positive linear operators. Math Ann. 1980;246:205–224.

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