On the second real eigenvalue of nonegative and Z-matrices

Linear Algebra and Its Applications

Volumn 255, Issue 1-3, 1997, Pages 303-313

  Friedland, Shmuel ^a   Nabben, Reinhard ^b  

^a UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

^b BIELEFELD UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040350301     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(96)00033-X     Document Type: Article

References (9)

1. J. Cheeger, A lower bound for the smallest eigenvalue of the Laplacian, in Problems in Analysis (R. C. Gunning, Ed.), Princeton U.P., 1970, pp. 195-199.
2. S. Friedland, The reconstruction of a symmetric matrix from the spectral data, J. Math. Anal. Appl. 71:412-422 (1979).
3. S. Friedland, Lower bounds for the first eigenvalue of certain M-matrices associated with graphs, Linear Algebra Appl. 172:71-84 (1992).
4. S. Friedland and L. Gurvits, Upper bound for the real part of nonmaximal eigenvalues of nonnegative irreducible matrices, SIAM J. Matrix Anal. Appl. 15:1015-1017 (1994).
5. M. Fiedler and T. L. Markham, A classification of matrices of class Z, Linear Algebra Appl. 173:115-124 (1992).
6. R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge U.P., Cambridge, 1985.
7. D. M. Koteljansldi, On some properties of matrices with positive elements, Amer. Math. Soc. Transl. Ser. 2 27:9-18 (1963).
8. R. Nabben, Z-matrices and inverse Z-matrices, Linear Algebra Appl., to appear.
9. R. L. Smith, Bounds on the spectrum of nonnegative matrices and certain Z-matrices, Linear Algebra Appl. 129:13-28 (1990).