On group inverses of M-matrices with uniform diagonal entries

Linear Algebra and Its Applications

Volumn 296, Issue 1-3, 1999, Pages 153-170

  Kirkland, Stephen J ^a   Neumann, Michael ^b  

^a UNIVERSITY OF REGINA   (Canada)

^b UNIVERSITY OF CONNECTICUT   (United States)

Author keywords

Group inverse; Laplacian; M matrix; Tree

Indexed keywords

EID: 0033413735     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(99)00127-5     Document Type: Article

References (13)

1. A. Ben-Israel, T.N. Greville, Generalized Inverses: Theory and Applications, Academic Press, New York, 1973.
2. A. Berman, R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia, 1994.
3. S.L. Campbell, C.D. Meyer Jr., Generalized Inverses of Linear Transformations, Dover Publications, New York, 1991.
4. S.W. Drury, G.P.H. Styan, G.E. Subak-Sharpe, On spanning trees and terminal weight numbers, McGill University, Department of Math, and Stats., Montreal, Canada, 1994 (Report 94-4).
5. C.R. Johnson, R. Loewy, D.D. Olesky, P. van den Driessche, Maximizing the spectral radius of fixed trace diagonal perturbations of nonnegative matrices, Linear Algebra Appl. 241-243 (1996) 635-654.
6. J.G. Kemeny, J.L. Snell, Finite Markov Chains, Van Nostrand, Princeton, NJ, 1959.
7. S.J. Kirkland, M. Neumann, Cutpoint decoupling and first passage times for random walks on graphs, SIAM J. Matrix Anal., 20 (1999) 60-70.
8. S.J. Kirkland, M. Neumann, Extremal first mean passage and variance times for trees, Random Structures and Algorithms, submitted.
9. S.J. Kirkland, M. Neumann, B. Shader, 1996. Bounds on the subdominant eigenvalue involving group inverses with applications to graphs, Czech. Math. J. 47 (1998) 1-20.
10. S.J. Kirkland, M. Neumann, B. Shader, Distances in weighted trees and group inverses of Laplacian matrices, SIAM J. Matrix. Anal. Appl. 18 (1997) 827-841.
11. C.D. Meyer Jr., The role of the group generalized inverse in the theory of finite Markov chains, SIAM Rev. 17 (1975) 443-464.
12. C.D. Meyer Jr., The condition of a finite Markov chain and perturbations bounds for the limiting probabilities, SIAM J. Alg. Disc. Meth. 1 (1980) 273-283.
13. G.P.H. Styan, G. Subak-Sharpe, Inequalities and equalities associated with the Campbell-Youla generalized inverse of the indefinite-admittance matrix and on its significance for metric structure, Linear Algebra Appl. 250 (1996) 349-370.