On some matrix inequalities

Xingzhi Zhan

doi:10.1016/j.laa.2003.08.008

On some matrix inequalities

Xingzhi Zhan

School of Mathematical Sciences

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

26 Scopus citations

Abstract

The arithmetic-geometric mean inequality for singular values due to Bhatia and Kittaneh says that 2s_j(AB*) ≤ s_j(A*A + B*B), j = 1, 2, ... for any matrices A, B. We first give new proofs of this inequality and its equivalent form. Then we use it to prove the following trace inequality: let A₀ be a positive definite matrix and A ₁,..., A_k be positive semidefinite matrices. Then tr ∑_j=1^k (∑_i=0^jA _i^-2) A_j < tr A₀^-1.

Original language	English
Pages (from-to)	299-303
Number of pages	5
Journal	Linear Algebra and Its Applications
Volume	376
Issue number	1-3
DOIs	https://doi.org/10.1016/j.laa.2003.08.008
State	Published - 1 Jan 2004

Keywords

Norm
Singular value
Trace inequalities

Access to Document

10.1016/j.laa.2003.08.008

Cite this

@article{c4cf3cfa644f4d178a247df63b5f2f6a,

title = "On some matrix inequalities",

abstract = "The arithmetic-geometric mean inequality for singular values due to Bhatia and Kittaneh says that 2sj(AB*) ≤ sj(A*A + B*B), j = 1, 2, ... for any matrices A, B. We first give new proofs of this inequality and its equivalent form. Then we use it to prove the following trace inequality: let A0 be a positive definite matrix and A 1,..., Ak be positive semidefinite matrices. Then tr ∑j=1k (∑i=0jA i-2) Aj < tr A0-1.",

keywords = "Norm, Singular value, Trace inequalities",

author = "Xingzhi Zhan",

year = "2004",

month = jan,

day = "1",

doi = "10.1016/j.laa.2003.08.008",

language = "英语",

volume = "376",

pages = "299--303",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

publisher = "Elsevier Inc.",

number = "1-3",

}

TY - JOUR

T1 - On some matrix inequalities

AU - Zhan, Xingzhi

PY - 2004/1/1

Y1 - 2004/1/1

N2 - The arithmetic-geometric mean inequality for singular values due to Bhatia and Kittaneh says that 2sj(AB*) ≤ sj(A*A + B*B), j = 1, 2, ... for any matrices A, B. We first give new proofs of this inequality and its equivalent form. Then we use it to prove the following trace inequality: let A0 be a positive definite matrix and A 1,..., Ak be positive semidefinite matrices. Then tr ∑j=1k (∑i=0jA i-2) Aj < tr A0-1.

AB - The arithmetic-geometric mean inequality for singular values due to Bhatia and Kittaneh says that 2sj(AB*) ≤ sj(A*A + B*B), j = 1, 2, ... for any matrices A, B. We first give new proofs of this inequality and its equivalent form. Then we use it to prove the following trace inequality: let A0 be a positive definite matrix and A 1,..., Ak be positive semidefinite matrices. Then tr ∑j=1k (∑i=0jA i-2) Aj < tr A0-1.

KW - Norm

KW - Singular value

KW - Trace inequalities

UR - https://www.scopus.com/pages/publications/0142094020

U2 - 10.1016/j.laa.2003.08.008

DO - 10.1016/j.laa.2003.08.008

M3 - 文章

AN - SCOPUS:0142094020

SN - 0024-3795

VL - 376

SP - 299

EP - 303

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1-3

ER -

On some matrix inequalities

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this