Moore-Penrose inverse of matrices on idempotent semirings

SIAM Journal on Matrix Analysis and Applications

Volumn 22, Issue 2, 2001, Pages 617-626

  Pati, S ^a  

^a UNIVERSITY OF REGINA   (Canada)

Author keywords

(max, +) semiring; (max, x) semiring; Boolean algebra; Moore Penrose inverse

Indexed keywords

EID: 0041409989     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479899355517     Document Type: Article

References (15)

1. F. BACCELI, G. COHEN, G. J. OLSDER, AND J. P. QUADRAT, Synchronization and Linearity, John Wiley and Sons, New York, 1992.
2. R. B. BAPAT, A max version of the Perron-Frobenius theorem, Linear Algebra Appl., 275/276 (1998), pp. 3-18.
3. R. B. BAPAT, D. P. STANFORD, AND P. VAN DEN DRIESSCHE, Pattern properties and spectral inequalities in max algebra, SIAM J. Matrix Anal. Appl., 16 (1995), pp. 964-976.
4. R. B. BAPAT, S. K. JAIN, AND S. PATI, Weighted Moore-Penrose inverse of a boolean matrix, Linear Algebra Appl., 255 (1997), pp. 267-279.
5. A. BERMAN AND R. J. PLEMMONS, Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia, 1994.
6. R. A. CUNINGHAME-GREEN, Minimax Algebra, Lecture Notes in Econom. and Math. Systems 166, Springer-Verlag, Berlin, Germany, 1979.
7. P. I. DUDINIKOV AND S. N. SAMBORSKII, Endomorphisms of finitely generated free semirings, Advances in Soviet Mathematics, 13 (1992), pp. 65-85.
8. S. GAUBERT, Methods and Applications of (max, +) Linear Algebra, Lecture Notes in Comput. Sci. 1200, Springer, Berlin, 1997.
9. S. GAUBERT, Théorie des Systémes Linéaires dans des Dioïdes, Ph.D. Thesis, L'Ecole des Mines de Paris, Paris, France, 1992.
10. M. GONDRAN AND M. MINOUX, Graphs and Algorithms, John Wiley and Sons, Chichester, UK, 1984.
11. M. GONDRAN AND M. MINOUX, Linear algebra in dioids: A survey of recent results, Ann. of Discrete Math., 19 (1984), pp. 147-163.
12. R. M. KARP, A characterization of the minimum cycle mean in a digraph, Discrete Math., 23 (1978), pp. 309-311.
13. K. H. KIM, Boolean Matrix Theory and Applications, Marcel Dekker, New York, 1982.
14. P.S.S.N.V.P. RAO AND K.P.S.B. RAO, On generalized inverses of boolean matrices, Linear Algebra Appl., 11 (1975), pp. 135-153.
15. W. CHEN, X. QI, AND S. DENG, The eigen problem and period analysis of the discrete event system, Systems Sci. Math. Sci., 3 (1990), pp. 243-260.