Mathematics Faculty Articles

Title

On Eigenvalue and Singular Value Inequalities for Matrix Product

Document Type

Article

Publication Date

1-1-1987

Publication Title

Journal of Beijing Normal University

Keywords

Matrix, Eigenvalue, Singular value

ISSN

0476-0301

Volume

1987

Issue/No.

3

First Page

1

Last Page

4

Abstract

Let H∈Cn×n have real eigenvalues λ1(H)≥⋯≥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).

Comments

Alternate Title: Beijing Shifan Daxue Xuebao (Ziran Kexue Ban)

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