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Linear and Multilinear Algebra Volume 28, 1991 - Issue 4
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Original Articles

The reachability cones of essentially nonnegative matrices

Michael Neumann Department of Mathematics, University of Connecticut, Storrs, CT, 06269-3009
,
Ronald J. Stern Department of Mathematics, Concordia University, Montreal, H4X 1J7, Canada
&
Michael J. Tsatsomeros Department of Mathematics, University of Connecticut, Storrs, CT, 06269-3009
Pages 213-224 | Received 19 Jan 1990, Published online: 02 Apr 2008

References

  • Bellman , R. 1960 . Introduction to Matrix Analysis , McGraw-Hill .
  • Berman , A. , Neumann , M. and Stern , R. J. 1986 . Cone reachability for nondiagonable linear differential systems . Lin. Alg. Appl. , 81 : 263 – 280 .
  • Berman , A. , Neumann , M. and Stern , R. J. 1989 . Nonnegative Matrices in Dynamic Systems , Wiley Interscience .
  • Birkhoff , G. and Varga , R. S. 1958 . Reactor criticality and non-negative matrices . J. Soc. Industr. Appl. Math. , 6 : 354 – 377 .
  • Hartwig , R. E. , Neumann , M. and Rose , N. J. 1990 . An algebraic-analytic approach to nonnegative bases . Lin. Alg. Appl. , 133 : 77 – 88 .
  • Neumann , M. and Stern , R. J. 1985 . Boundary results for positively invariant cones and their reachability cones . Lin. Mult. Alg. , 17 : 143 – 154 .
  • Neumann , M. and Stern , R. J. 1986 . Cone reachability for linear differential systems . Applicable Anal. , 20 : 57 – 71 .
  • Neumann , M. and Stern , R. J. 1989 . Discrete approximations to reachability cones of linear differential systems . Lin. Alg. Appl. , 120 : 65 – 79 .
  • Richman , D. and Schneider , H. 1978 . On the singular graph and the Weyr characteristic of an M -matrix . Aequationes Math. , 17 : 208 – 234 .
  • Rockafellar , R. 1970 . Convex Analysis , UP : Princeton .
  • Rothblum , U. 1975 . Algebraic eigenspaces of nonnegative matrices . Lin. Alg. Appl. , 12 : 281 – 292 .
  • Schneider , H. and Vidyasagar , M. 1970 . Cross positive matrices . SIAM J. Num. Anal. , 7 : 508 – 519 .
  • Stern , R. J. 1981 . Generalized M-matrices . Lin. Alg. Appl. , 41 : 201 – 208 .

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