Some New Bounds for the Eigenvalues of Hadamard Product of Two Irreducible M-matrices
To study the lower bound for the minimum eigenvalue and a upper bound for the spectral radius of Hadamard product of two irreducible M-matrices A and B , obtaining some new estimation of the bounds. These new bounds are only depend on the element of A and B, so they are easy to calculate.
Unable to display preview. Download preview PDF.
- 1.M. Fiedler, T.L. Markham, An inequality for the Hadamard product of an M-matrix, Linear Algebra Appl. 101 (1988) 1–8.Google Scholar
- 2.M. Fiedler, C.R. Johnson, T.L. Markham, M. Neumann, A trace inequality for M - matrices and the symmetrizability of a real matrix by a positive diagonal matrix, Linear Algebra Appl. 71 (1985) 81–94.Google Scholar
- 3.X.R. Yong, Proof of a conjecture of Fiedler and Markham. Linear Algebra Appl. 320 (2000) 167–171.Google Scholar
- 4.Y.Z. Song, On an inequality for the Hadamard product of an M-matrix, Linear Algebra Appl. 305 (2000) 99–105.Google Scholar
- 5.S.C. Chen, A lower bound for the minimum eigenvalue of the Hadamard product of matrix, Linear Algebra Appl. 378 (2004) 159–166.Google Scholar
- 6.H.B. Li, T.Z. Huang, S.Q. Shen, H. Li, Lower bounds for the eigenvalue of Hadamard product of an M-matrix and its inverse, Linear Algebra Appl. 420 (2007) 235–247.Google Scholar
- 7.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.Google Scholar
- 8.Y.T. Li, Y.Y. Li, R.W. Wang, Y.Q. Wang, Some new bounds on eigenvalues of the Hadamard product and the Fan product of matrices, Linear Algebra Appl. 432(2010)536–545.Google Scholar
- 9.R.S. Varga, Minimal Gerschgorin sets, Pacific J. Math. 15(2) (1965) 719–729.Google Scholar
- 10.X.R. Yong, Z. Wang, On a a conjecture of Fiedler and Markham, Linear Algebra Appl. 288(1999)259–267.Google Scholar