A new
inequality on the minimum eigenvalue for the Fan product of nonsingular M-matrices is given. In addition, a new
inequality on the spectral radius of the Hadamard product of nonnegative
matrices is also obtained. These inequalities can improve considerably some
previous results.
References
[1]
Berman, A. and Plemmons, R.J. (1979) Nonnegaive Matrices in the Mathematical Sciences. Academic Press, New York.
[2]
Horn, R.A. and Johnson, C.R. (1985) Topics in Matrix Analysis. Cambridge University Press, Cambridge. http://dx.doi.org/10.1017/CBO9780511810817
[3]
Fang, M.Z. (2007) Bounds on Eigenvalues for the Hadamard Product and the Fan Product of Matrices. Linear Algebra and its Applications, 425, 7-15. http://dx.doi.org/10.1016/j.laa.2007.03.024
[4]
Huang, R. (2008) Some Inequalities for the Hadamard Product and the Fan Product of Matrices. Linear Algebra and its Applications, 428, 1551-1559. http://dx.doi.org/10.1016/j.laa.2007.10.001
[5]
Li, Y.T., Li, Y.Y., Wang, R.W. and Wang, Y.Q. (2010) Some New Lower Bounds on Eigenvalues of the Hadamard Product and the Fan Product of Matrices. Linear Algebra and its Applications, 432, 536-545. http://dx.doi.org/10.1016/j.laa.2009.08.036
[6]
Liu, Q.B. and Chen, G.L. (2009) On Two Inequalities for the Hadamard Product and the Fan Product of Matrices. Linear Algebra and its Applications, 431, 974-984. http://dx.doi.org/10.1016/j.laa.2009.03.049
[7]
Liu, Q.B., Chen, G.L. and Zhao, L.L. (2010) Some New Bounds on the Spectral Radius of Matrices. Linear Algebra and its Applications, 432, 936-948. http://dx.doi.org/10.1016/j.laa.2009.10.006
[8]
Zhou, D.M., Chen, G.L., Wu, G.X. and Zhang, X.Y. (2013) On Some New Bounds for Eigenvalues of the Hadamard Product and the Fan Product of Matrices. Linear Algebra and its Applications, 438, 1415-1426. http://dx.doi.org/10.1016/j.laa.2012.09.013
[9]
Zhao, L.L. (2012) Two Inequalities for the Hadamard Product of Matrices. Journal of Inequalities and Applications, 2012, 1-7. http://dx.doi.org/10.1186/1029-242X-2012-122
Berman, A. and Plemmons, R.J. (1994) Nonnegaive Matrices in the Mathematical Sciences. SIAM, Philadelphia. http://dx.doi.org/10.1137/1.9781611971262
[12]
Brauer, A. (1947) Limits for the Characteristic Roots of a Matrix Ⅱ. Duke Mathematical Journal, 14, 21-26. http://dx.doi.org/10.1215/S0012-7094-47-01403-8