Some new bounds on eigenvalues of the Hadamard product and the Fan product of matrices

Yao tang Li; Yan yan Li; Rui Wu Wang; Ya qiang Wang

doi:10.1016/j.laa.2009.08.036

Some new bounds on eigenvalues of the Hadamard product and the Fan product of matrices

Yao tang Li, Yan yan Li, Rui Wu Wang, Ya qiang Wang

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

22 Scopus citations

Abstract

Let A and B be nonsingular M-matrices. A lower bound on the minimum eigenvalue q (B {ring operator} A^{- 1}) for the Hadamard product of A^{- 1} and B, and a lower bound on the minimum eigenvalue q (A {star, open} B) for the Fan product of A and B are given. In addition, an upper bound on the spectral radius ρ (A {ring operator} B) of nonnegative matrices A and B is also obtained. These bounds improve several existing results in some cases and the estimating formulas are easier to calculate for they are only depending on the entries of matrices A and B.

Original language	English
Pages (from-to)	536-545
Number of pages	10
Journal	Linear Algebra and Its Applications
Volume	432
Issue number	2-3
DOIs	https://doi.org/10.1016/j.laa.2009.08.036
State	Published - 15 Jan 2010
Externally published	Yes

Keywords

Fan product
Hadamard product
M-matrix
Minimum eigenvalue
Nonnegative matrix
Spectral radius

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10.1016/j.laa.2009.08.036

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abstract = "Let A and B be nonsingular M-matrices. A lower bound on the minimum eigenvalue q (B {ring operator} A- 1) for the Hadamard product of A- 1 and B, and a lower bound on the minimum eigenvalue q (A {star, open} B) for the Fan product of A and B are given. In addition, an upper bound on the spectral radius ρ (A {ring operator} B) of nonnegative matrices A and B is also obtained. These bounds improve several existing results in some cases and the estimating formulas are easier to calculate for they are only depending on the entries of matrices A and B.",

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T1 - Some new bounds on eigenvalues of the Hadamard product and the Fan product of matrices

AU - Li, Yao tang

AU - Li, Yan yan

AU - Wang, Rui Wu

AU - Wang, Ya qiang

PY - 2010/1/15

Y1 - 2010/1/15

N2 - Let A and B be nonsingular M-matrices. A lower bound on the minimum eigenvalue q (B {ring operator} A- 1) for the Hadamard product of A- 1 and B, and a lower bound on the minimum eigenvalue q (A {star, open} B) for the Fan product of A and B are given. In addition, an upper bound on the spectral radius ρ (A {ring operator} B) of nonnegative matrices A and B is also obtained. These bounds improve several existing results in some cases and the estimating formulas are easier to calculate for they are only depending on the entries of matrices A and B.

AB - Let A and B be nonsingular M-matrices. A lower bound on the minimum eigenvalue q (B {ring operator} A- 1) for the Hadamard product of A- 1 and B, and a lower bound on the minimum eigenvalue q (A {star, open} B) for the Fan product of A and B are given. In addition, an upper bound on the spectral radius ρ (A {ring operator} B) of nonnegative matrices A and B is also obtained. These bounds improve several existing results in some cases and the estimating formulas are easier to calculate for they are only depending on the entries of matrices A and B.

KW - Fan product

KW - Hadamard product

KW - M-matrix

KW - Minimum eigenvalue

KW - Nonnegative matrix

KW - Spectral radius

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DO - 10.1016/j.laa.2009.08.036

M3 - 文章

AN - SCOPUS:70449678625

SN - 0024-3795

VL - 432

SP - 536

EP - 545

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 2-3

ER -

Some new bounds on eigenvalues of the Hadamard product and the Fan product of matrices

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Keywords

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