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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

Stability and semipositivity of real matrices


Authors: Abraham Berman and Robert C. Ward
Journal: Bull. Amer. Math. Soc. 83 (1977), 262-263
MSC (1970): Primary 15A48; Secondary 15A15, 15A18, 65F15, 93D05
MathSciNet review: 0422309
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  • 1. G . P. Barker, A. Berman, and R. J. Plemmons, Positive diagonal solutions to the Lyapunov equations, Linear and Multilinear Algebra 5 (1977/78), no. 4, 249–256. MR 0469939 (57 #9719)
  • 2. Miroslav Fiedler and Vlastimil Pták, On matrices with non-positive off-diagonal elements and positive principal minors, Czechoslovak Math. J. 12 (87) (1962), 382–400 (English, with Russian summary). MR 0142565 (26 #134)
  • 3. Charles R. Johnson, Second, third, and fourth order 𝐷-stability, J. Res. Nat. Bur. Standards Sect. B 78B (1974), 11–13. MR 0340287 (49 #5042)
  • 4. A. M. Lyapunov (1892), Problème général de la stabilité du mouvement, Comm. Math. Soc. Kharkow; English transl., Ann. of Math. Studies, no. 17, Princeton Univ. Press, Princeton, N. J.; Oxford Univ. Press, London, 1947. MR 9, 34.
  • 5. Olga Taussky, A remark on a theorem of Lyapunov, J. Math. Anal. Appl. 2 (1961), 105–107. MR 0124335 (23 #A1649)
  • 6. James S. Vandergraft, Applications of partial orderings to the study of positive definiteness, monotonicity, and convergence of iterative methods for linear systems, SIAM J. Numer. Anal. 9 (1972), 97–104. MR 0309971 (46 #9074)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9904-1977-14295-X
PII: S 0002-9904(1977)14295-X