Revisit on spectral geometric mean

Gan, Luyining; Kim, Sejong

doi:10.1080/03081087.2023.2171353

Linear and Multilinear Algebra

2023

DOI: 10.1080/03081087.2023.2171353

|View full text |Cite

Revisit on spectral geometric mean

Luyining Gan

Sejong Kim

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2023

2024

Publication Types

Select...

Article5

Relationship

Self Cite0

Independent5

Authors

Journals

Cited by 5 publications

(1 citation statement)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, Gan, Liu, and Tam [8] and Gan and Tam [9] studied A t B and obtained some nice properties. A nice survey and new properties related to the weighted spectral geometric mean A t B can be found in the recent paper of Gan and Kim [7].…”

mentioning

confidence: 99%

A new weighted spectral geometric mean and properties

Dinh,

Tam,

Vuong

2024

ELA

View full text Add to dashboard Cite

In this paper, we introduce a new weighted spectral geometric mean: \begin{equation*}\label{F-mean}F_t(A,B)= (A^{-1}\sharp_t B)^{1/2} A^{2-2t} (A^{-1} \sharp_t B)^{1/2}, \quad t\in [0,1],\end{equation*} where $A$ and $B$ are positive definite matrices. We study basic properties and inequalities for $F_t(A, B)$. We also establish the Lie-Trotter formula for $F_t(A, B)$. Finally, we extend some of the results on $F_t(A, B)$ to symmetric space of noncompact types.

show abstract

mentioning

confidence: 99%

A new weighted spectral geometric mean and properties

Dinh,

Tam,

Vuong

2024

ELA

View full text Add to dashboard Cite

show abstract

Near order and metric-like functions on the cone of positive definite matrices

Dumitru,

Franco

2023

Positivity

View full text Add to dashboard Cite

Near-order relation of power means

Hwang,

Kim

2024

Positivity

View full text Add to dashboard Cite

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Revisit on spectral geometric mean

Cited by 5 publications

References 15 publications

A new weighted spectral geometric mean and properties

A new weighted spectral geometric mean and properties

Near order and metric-like functions on the cone of positive definite matrices

Near-order relation of power means

Contact Info

Product

Resources

About