Some Inequalities for Sum and Product of Positive Semidefinite Matrices

Bo-Ying Wang; Bo-Yan Xi; Fuzhen Zhang

doi:10.1016/S0024-3795(99)00013-0

Some Inequalities for Sum and Product of Positive Semidefinite Matrices

Bo-Ying Wang
, Bo-Yan Xi
, Fuzhen Zhang

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

11 Scopus citations

Abstract

The purpose of this paper is to present some inequalities on majorization, unitarily invariant norm, trace, and eigenvalue for sum and product of positive semidefinite (Hermitian) matrices. Some open questions proposed by Marshall and Olkin are resolved.

Original language	American English
Journal	Linear Algebra and its Applications
Volume	293
DOIs	https://doi.org/10.1016/S0024-3795(99)00013-0
State	Published - May 15 1999

Keywords

Eigenvalue
Inequality
Majorization
Moore-Penrose inverse
Positive semidefinite matrix
Singular value
Unitarily invariant norm

Disciplines

Mathematics

Access to Document

10.1016/S0024-3795(99)00013-0License: Unspecified

http://www.sciencedirect.com/science/article/pii/S0024379599000130

Cite this

@article{063d7af46afb4e4d85e6cd5fdfb310e5,

title = "Some Inequalities for Sum and Product of Positive Semidefinite Matrices",

abstract = " The purpose of this paper is to present some inequalities on majorization, unitarily invariant norm, trace, and eigenvalue for sum and product of positive semidefinite (Hermitian) matrices. Some open questions proposed by Marshall and Olkin are resolved.",

keywords = "Eigenvalue, Inequality, Majorization, Moore-Penrose inverse, Positive semidefinite matrix, Singular value, Unitarily invariant norm",

author = "Bo-Ying Wang and Bo-Yan Xi and Fuzhen Zhang",

year = "1999",

month = may,

day = "15",

doi = "10.1016/S0024-3795(99)00013-0",

language = "American English",

volume = "293",

journal = "Linear Algebra and its Applications",

issn = "0024-3795",

publisher = "Elsevier Inc.",

}

TY - JOUR

T1 - Some Inequalities for Sum and Product of Positive Semidefinite Matrices

AU - Wang, Bo-Ying

AU - Xi, Bo-Yan

AU - Zhang, Fuzhen

PY - 1999/5/15

Y1 - 1999/5/15

N2 - The purpose of this paper is to present some inequalities on majorization, unitarily invariant norm, trace, and eigenvalue for sum and product of positive semidefinite (Hermitian) matrices. Some open questions proposed by Marshall and Olkin are resolved.

AB - The purpose of this paper is to present some inequalities on majorization, unitarily invariant norm, trace, and eigenvalue for sum and product of positive semidefinite (Hermitian) matrices. Some open questions proposed by Marshall and Olkin are resolved.

KW - Eigenvalue

KW - Inequality

KW - Majorization

KW - Moore-Penrose inverse

KW - Positive semidefinite matrix

KW - Singular value

KW - Unitarily invariant norm

UR - https://nsuworks.nova.edu/math_facarticles/110

UR - http://www.sciencedirect.com/science/article/pii/S0024379599000130

U2 - 10.1016/S0024-3795(99)00013-0

DO - 10.1016/S0024-3795(99)00013-0

M3 - Article

SN - 0024-3795

VL - 293

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

ER -

Some Inequalities for Sum and Product of Positive Semidefinite Matrices

Abstract

Keywords

Disciplines

Access to Document

Other files and links

Fingerprint

Cite this