Inverses of unipathic M-matrices

SIAM Journal on Matrix Analysis and Applications

Volumn 17, Issue 4, 1996, Pages 1025-1036

  McDonald, J J ^a   Neumann, M ^b   Schneider, H ^c   Tsatsomeros, M J ^a  

^a UNIVERSITY OF REGINA   (Canada)

^b UNIVERSITY OF CONNECTICUT   (United States)

^c UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

Inverse; M matrix; Principal minor; Unipathic digraph

Indexed keywords

EID: 0030510143     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479894277247     Document Type: Article

References (15)

1. W. W. BARRETT, A theorem on inverses of tridiagonal matrices, Linear Algebra Appl., 27 (1979), pp. 211-217.
2. A. BERMAN AND R. PLEMMONS, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, 1979.
3. R. A. BRUALDI AND H. SCHNEIDER, Determinantal identities: Gauss, Schur, Cauchy, Sylvester, Kronecker, Jacobi, Binet, Laplace, Muir, and Cayley, Linear Algebra Appl., 52/53 (1983), pp. 769-791.
4. M. FIEDLER, On inverting partitioned matrices, Czechoslovak Math. J., 13 (1963), pp. 574-586.
5. F. HARARY, R. Z. NORMAN, AND D. CARTWRIGHT, Structural Models, Wiley, New York, 1965.
6. C. R. JOHNSON, Inverse M-matrices, Linear Algebra Appl., 47 (1982), pp. 195-216.
7. M. LEWIN, Totally nonnegative, M-, and Jacobi matrices, SIAM J. Alg. Disc. Meth., 1 (1980), pp. 419-421.
8. M. LEWIN AND M. NEUMANN, The inverse M-matrix problem for (0, 1)-matrices, Linear Algebra Appl., 30 (1980), pp. 41-50.
9. T. J. LUNDY AND J. S. MAYBEE, Uniformly One-Connected Matrices and Their Inverses, preprint.
10. T. L. MARKHAM, Nonnegative matrices whose inverses are M-matrices, Proc. Amer. Math Soc., 36 (1972), pp. 326-330.
11. J. S. MAYBEE, Some possible new directions for combinatorial matrix analysis, Linear Algebra Appl., 107 (1988), pp. 23-40.
12. J. J. MCDONALD, M. NEUMANN, H. SCHNEIDER, AND M. J. TSATSOMEROS, Inverse M-matrix inequalities and generalized ultrametrix matrices, Linear Algebra Appl., 220 (1995), pp. 321-341.
13. H. SCHNEIDER, Theorems on M-splittings of a singular M-matrix which depend on graph structure, Linear Algebra Appl., 58 (1984), pp. 407-424.
14. L. J. WATFORD, JR., The Schur complement of generalized M-matrices, Linear Algebra Appl., 5 (1972), pp. 247-255.
15. R. A. WILLOUGHBY, The inverse M-matrix problem, Linear Algebra Appl., 18 (1977), pp. 75-94.