Characterization of symmetric M-matrices as resistive inverses

Linear Algebra and Its Applications

Volumn 430, Issue 4, 2009, Pages 1336-1349

  Bendito, E ^a   Carmona, A ^a   Encinas, A M ^a   Gesto, J M ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Effective resistance; Green kernels; Kirchhoff index; M matrices; Moore Penrose inverse; Schr dinger operators

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS;

EFFECTIVE RESISTANCE; GREEN KERNELS; KIRCHHOFF INDEX; M-MATRICES; MOORE-PENROSE INVERSE;

TURBULENT FLOW;

EID: 58049209661     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2008.10.027     Document Type: Article

References (19)

1. Balalli R., and Bapat R.B. On Euclidean distance matrices. Linear Algebra Appl. 424 (2007) 108-117
2. Bapat R.B. Resistance matrix of a weigthed graph. MATCH Commun. Math. Comput. Chem. 50 (2004) 73-82
3. Bapat R.B., and Raghavan T.E.S. Nonnegative Matrices and Applications (1997), Cambridge University Press, Cambridge, London
4. Bendito E., Carmona A., and Encinas A.M. Potential theory for Schrödinger operators on finite networks. Rev. Mat. Iberoamericana 21 (2005) 771-818
5. Bendito E., Carmona A., Encinas A.M., and Gesto J.M. Potential theory for boundary value problems on finite networks. Appl. Anal. Discrete Math. 1 (2007) 299-310
6. Dellacherie C., Martínez S., and San Martín J. Ultrametric matrices and induced Markov chains. Adv. Appl. Math. 17 (1996) 169-183
7. Dellacherie C., Martínez S., and San Martín J. Description of the sub-Markov kernel associated to generalized ultrametric matrices. An algorithmic approach. Linear Algebra Appl. 318 (2000) 1-21
8. Fiedler M. Some characterizations of symmetric inverse M-matrices. Linear Algebra Appl. 275-276 (1998) 179-187
9. Fiedler M. Special ultrametric matrices and graphs. SIAM J. Matrix Anal. Appl. 22 (2000) 106-113
10. Ghosh A., Boyd S., and Saberi A. Minimizing effective resistance of a graph. SIAM Rev. 50 (2008) 37-66
11. Gutman I., and Xiao W. Generalized inverse of the Laplacian matrix and some applications. Bull. Cl. Sci. Math. Nat. Sci. Math. 29 (2004) 15-23
12. Kirkland S.J., and Neumann M. The M-matrix group generalized inverse problem for weighted trees. SIAM J. Matrix Anal. Appl. 19 (1998) 226-234
13. Kirkland S.J., Neumann M., and Shader B.L. Distance in weigthed trees and group inverse of Laplacian matrices. SIAM J. Matrix Anal. Appl. 18 (1997) 827-841
14. Martínez S., Michon G., and San Martín J. Inverses of ultrametric matrices are of Stieltjes type. SIAM J. Matrix Anal. Appl. 15 (1994) 98-106
15. McDonald J.J., Neumann M., Schneider H., and Tsatsomeros M.J. Inverse M-matrix inequalities and generalized ultrametric matrices. Linear Algebra Appl. 220 (1995) 321-341
16. Nabben R., and Varga R.S. A linear algebra proof that the inverse of a strictly ultrametric matrix is a strictly diagonally dominant Stieltjes matrix. SIAM J. Matrix Anal. Appl. 15 (1994) 107-113
17. Nabben R., and Varga R.S. Generalized ultrametric matrices - a class of inverse M-matrices. Linear Algebra Appl. 220 (1995) 365-390
18. Styan G.P.H., and Subak-Sharpe G.E. Inequalities and equalities associated with the Campbell-Youla generalized inverse of the indefinite admittance matrix of resistive networks. Linear Algebra Appl. 250 (1997) 349-370
19. Xiao W., and Gutman I. Resistance distance and Laplacian spectrum. Theor. Chem. Acc. 110 (2003) 284-289