• 検索結果がありません。

BOUNDSONTHESPECTRALRADIUSOFAHADAMARDPRODUCTOFNONNEGATIVEORPOSITIVESEMIDEFINITEMATRICES ELA

N/A
N/A
Info
ダウンロード
Protected

Academic year: 2022

シェア "BOUNDSONTHESPECTRALRADIUSOFAHADAMARDPRODUCTOFNONNEGATIVEORPOSITIVESEMIDEFINITEMATRICES ELA"

Copied!
1
0
0

読み込み中.... (全文を見る)

今ダウンロードする ( 1 ページ )

全文

(1)

ELA

BOUNDS ON THE SPECTRAL RADIUS OF A HADAMARD PRODUCT OF NONNEGATIVE OR

POSITIVE SEMIDEFINITE MATRICES

∗

ROGER A. HORN† AND FUZHEN ZHANG‡

Abstract. X. Zhan has conjectured that the spectral radius of the Hadamard product of two square nonnegative matrices is not greater than the spectral radius of their ordinary product. We prove Zhan’s conjecture, and a related inequality for positive semidefinite matrices, using standard facts about principal submatrices, Kronecker products, and the spectral radius.

Key words. Hadamard product, Nonnegative matrix, Positive semidefinite matrix, Positive definite matrix, Spectral radius, Kronecker product, Matrix inequality.

AMS subject classifications. 15A45, 15A48, 15A69.

∗Received by the editors November 4, 2009. Accepted for publication February 8, 2010. Handling Editor: Bit-Shun Tam.

†Mathematics Department, University of Utah, Salt Lake City, Utah 84112, USA ([email protected]).

‡Division of Math, Science and Technology, Nova Southeastern University, Fort Lauderdale, Florida 33314, USA ([email protected]).

Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 20, pp. 90-94, February 2010

http://math.technion.ac.il/iic/ela

参照

今ダウンロードする ( PDF - 1 ページ - 22.85 KB )

関連したドキュメント

Necessary and sufficient conditions for the equivalence and congruence of matrices under the action of standard parabolic subgroups are discussed

EQUIVALENCE AND CONGRUENCE OF MATRICES UNDER THE ACTION OF STANDARD PARABOLIC SUBGROUPS ∗.. FERNANDO

Roman Drnovˇsek *K@I BH JDA IFA?JH= H=@EKI B FIEJELA FAH=JHI

An application of our results gives simple upper and lower bounds for the spectral radius of a product of positive operators in terms of positive eigenvectors corresponding to

Semi-Presentations for the Sporadic Simple Groups

To prove that a given allowable pair is actually a pair of standard generators, we use the following facts about G (which can be derived from the character table and power maps of

LihuaFengandGuihaiYu ONTHREECONJECTURESINVOLVINGTHESIGNLESSLAPLACIANSPECTRALRADIUSOFGRAPHS

We study the signless Laplacian spectral radius of graphs and prove three conjectures of Cvetković, Rowlinson, and Simić [Eigenvalue bounds for the signless Laplacian,

Laplacian Spectral Radius And Some Hamiltonian Properties Of Graphs

Using an upper bound for the Laplacian spectral radius of graphs obtained by Shu et al., we in this note present su¢ cient conditions which are based on the Laplacian spectral

We introduce the concept of (k, l)-radius of a graph and prove that for any fixed pairk, lthe (k, l)-radius is equal to 2 k2 − l 2 for almost all graphs

The transmission of the graph, also called a distance of the graph, is defined as the sum of distances between all pairs of vertices (for general properties of the distance see

Graphs with Given Degree Sequence and Maximal Spectral Radius

The results are related to the (partly open) problem of finding connected graphs of maximal spectral radius with given number of vertices and edges (but arbitrary degree

THE SPECTRAL CONJECTURE.∗ ALAN KRAUTSTENGL† AND RICHARD S

In an earlier paper from 1970, entitled “Minimal Gerschgorin sets for partitioned matrices,” a Spectral Conjecture, related to norms and spectral radii of special partitioned