Extension of block matrix representation of the geometric mean

Hana Choi; Hayoung Choi; Sejong Kim; Hosoo Lee

doi:10.4134/JKMS.j190272

Extension of block matrix representation of the geometric mean

Hana Choi, Hayoung Choi, Sejong Kim, Hosoo Lee

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

Abstract

To extend the well-known extremal characterization of the geometric mean of two n × n positive definite matrices A and B, we solve the following problem: [formula presented] We find an explicit expression of the maximum value with respect to the matrix geometric mean of Schur complements.

Original language	English
Pages (from-to)	641-653
Number of pages	13
Journal	Journal of the Korean Mathematical Society
Volume	57
Issue number	3
DOIs	https://doi.org/10.4134/JKMS.j190272
State	Published - 2020

Keywords

Matrix geometric mean
Positive matrix completion
Schur complement

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10.4134/JKMS.j190272

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title = "Extension of block matrix representation of the geometric mean",

abstract = "To extend the well-known extremal characterization of the geometric mean of two n × n positive definite matrices A and B, we solve the following problem: [formula presented] We find an explicit expression of the maximum value with respect to the matrix geometric mean of Schur complements.",

keywords = "Matrix geometric mean, Positive matrix completion, Schur complement",

author = "Hana Choi and Hayoung Choi and Sejong Kim and Hosoo Lee",

note = "Publisher Copyright: {\textcopyright} 2020 Korean Mathematical Society.",

year = "2020",

doi = "10.4134/JKMS.j190272",

language = "English",

volume = "57",

pages = "641--653",

journal = "Journal of the Korean Mathematical Society",

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publisher = "Korean Mathematical Society",

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TY - JOUR

T1 - Extension of block matrix representation of the geometric mean

AU - Choi, Hana

AU - Choi, Hayoung

AU - Kim, Sejong

AU - Lee, Hosoo

PY - 2020

Y1 - 2020

N2 - To extend the well-known extremal characterization of the geometric mean of two n × n positive definite matrices A and B, we solve the following problem: [formula presented] We find an explicit expression of the maximum value with respect to the matrix geometric mean of Schur complements.

AB - To extend the well-known extremal characterization of the geometric mean of two n × n positive definite matrices A and B, we solve the following problem: [formula presented] We find an explicit expression of the maximum value with respect to the matrix geometric mean of Schur complements.

KW - Matrix geometric mean

KW - Positive matrix completion

KW - Schur complement

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U2 - 10.4134/JKMS.j190272

DO - 10.4134/JKMS.j190272

M3 - Article

AN - SCOPUS:85083873385

SN - 0304-9914

VL - 57

SP - 641

EP - 653

JO - Journal of the Korean Mathematical Society

JF - Journal of the Korean Mathematical Society

IS - 3

ER -

Extension of block matrix representation of the geometric mean

Abstract

Keywords

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