Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31515
Some New Inequalities for Eigenvalues of the Hadamard Product and the Fan Product of Matrices

Authors: Jing Li, Guang Zhou


Let A and B be nonnegative matrices. A new upper bound on the spectral radius ρ(A◦B) is obtained. Meanwhile, a new lower bound on the smallest eigenvalue q(AB) for the Fan product, and a new lower bound on the minimum eigenvalue q(B ◦A−1) for the Hadamard product of B and A−1 of two nonsingular M-matrices A and B are given. Some results of comparison are also given in theory. To illustrate our results, numerical examples are considered.

Keywords: Hadamard product, Fan product; nonnegative matrix, M-matrix, Spectral radius, Minimum eigenvalue, 1-path cover.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1665


[1] R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press, 1985.
[2] Y.T.Li, F.B.Chen, D.F.Wang, New lower bounds on eigenvalue of the Hadamard product of an M-matrix and its inverse, Linear Algebra Appl. 430(2009) 1423-1431.
[3] X.R.Yong, Z.Wang, On a conjecture of Fiedler and Markharm, Linear Algebra Appl. 288(1999) 259-267.
[4] H.B.Lu, Estimate for the Perron Root of a Nonnegative matrix, Chinese Journal of Engineering. Mathematices. 25(2008) 68-73.
[5] R.A.Horn, C.R.Johnson, Topics in Matrix Analysis,Cambridge University Press, 1991.
[6] R.Huang, Some inequalities of the Hadamard product and the Fan product of matrices. Linear Algebr.Appl. 2008, 428, 1551-1559.
[7] D.M.Zhou, G.L.Chen, G.X.Wu, X.Y.Zhang. On some new bounds for eigenvalues of the Hadamard product and the Fan product of matrices. Linear Algebra Appl, 2012, In Press.