On Eigenvalue and Singular Value Inequalities for Matrix Product

Bo-Ying Wang; Fuzhen Zhang

On Eigenvalue and Singular Value Inequalities for Matrix Product

Bo-Ying Wang
, Fuzhen Zhang

Department of Mathematics

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

Abstract

<p> Let H∈Cn×n have real eigenvalues λ1(H)≥&ctdot;≥λn(H). It is known that if G and H are two nonnegative matrices, then ∑kt=1λt(GH)≥∑kt=1λt(G)λn−t+1(H). The authors prove that in this case if 1≤i1 ∑t=1kλit(GH)≥∑t=1kλit(G)λn−t+1(H) and ∑t=1kλt(GH)≥∑t=1kλit(G)λn−it+1(H).</p>

Original language	American English
Journal	Journal of Beijing Normal University
Volume	1987
State	Published - Jan 1 1987

Keywords

Eigenvalue
Matrix
Singular value

Disciplines

Mathematics

Cite this

@article{01cdb93992744619b28f32d75d4feb58,

title = "On Eigenvalue and Singular Value Inequalities for Matrix Product",

abstract = " Let H\∈Cn\×n have real eigenvalues \λ1(H)\≥\&ctdot;\≥\λn(H). It is known that if G and H are two nonnegative matrices, then \∑kt=1\λt(GH)\≥\∑kt=1\λt(G)\λn\−t+1(H). The authors prove that in this case if 1\≤i1 \∑t=1k\λit(GH)\≥\∑t=1k\λit(G)\λn\−t+1(H) and \∑t=1k\λt(GH)\≥\∑t=1k\λit(G)\λn\−it+1(H).",

keywords = "Eigenvalue, Matrix, Singular value",

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

year = "1987",

month = jan,

day = "1",

language = "American English",

volume = "1987",

journal = "Journal of Beijing Normal University",

issn = "1002-0209",

}

TY - JOUR

T1 - On Eigenvalue and Singular Value Inequalities for Matrix Product

AU - Wang, Bo-Ying

AU - Zhang, Fuzhen

PY - 1987/1/1

Y1 - 1987/1/1

N2 - Let H∈Cn×n have real eigenvalues λ1(H)≥&ctdot;≥λn(H). It is known that if G and H are two nonnegative matrices, then ∑kt=1λt(GH)≥∑kt=1λt(G)λn−t+1(H). The authors prove that in this case if 1≤i1 ∑t=1kλit(GH)≥∑t=1kλit(G)λn−t+1(H) and ∑t=1kλt(GH)≥∑t=1kλit(G)λn−it+1(H).

AB - Let H∈Cn×n have real eigenvalues λ1(H)≥&ctdot;≥λn(H). It is known that if G and H are two nonnegative matrices, then ∑kt=1λt(GH)≥∑kt=1λt(G)λn−t+1(H). The authors prove that in this case if 1≤i1 ∑t=1kλit(GH)≥∑t=1kλit(G)λn−t+1(H) and ∑t=1kλt(GH)≥∑t=1kλit(G)λn−it+1(H).

KW - Eigenvalue

KW - Matrix

KW - Singular value

UR - https://nsuworks.nova.edu/math_facarticles/81

M3 - Article

SN - 1002-0209

VL - 1987

JO - Journal of Beijing Normal University

JF - Journal of Beijing Normal University

ER -

On Eigenvalue and Singular Value Inequalities for Matrix Product

Abstract

Keywords

Disciplines

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