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Rohn, Jiří
Nonsingularity and $P$-matrices. (English). Aplikace matematiky, vol. 35 (1990), issue 3, pp. 215-219
MSC: 15A03, 15A57, 65F99, 65G10, 65G30 | MR 1052742 | Zbl 0716.65046 | DOI: 10.21136/AM.1990.104405
Keywords:
nonsingular matrices; $P$-matrices
Summary:
New proofs of two previously published theorems relating nonsingularity of interval matrices to $P$-matrices are given.
References:
[1] M. Fiedler: Special Matrices and Their Use in Numerical Mathematics. (Czech). SNTL, Prague 1981.
[2] M. Fiedler V. Pták: On Matrices with Non-Positive Off-Diagonal Elements and Positive Principal Minors. Czechoslovak Math. J. 12 (1962), 382-400. MR 0142565
[3] D. Gale H. Nikaido: The Jacobian Matrix and Global Univalence of Mappings. Math. Annalen 159 (1965), 81-93. DOI 10.1007/BF01360282 | MR 0204592
[4] S. Poljak J. Rohn: Radius of Nonsingularity. KAM Series 88-117, Charles University, Prague 1988.
[5] J. Rohn: Systems of Linear Interval Equations. Lin. Alg. and Its Appls. 126 (1989), 39-78. DOI 10.1016/0024-3795(89)90004-9 | MR 1040771 | Zbl 0712.65029
[6] J. Rohn: Characterization of a Linear Program in Standard Form by a Family of Linear Programs with Inequality Constraints. To appear in Ekon.-Mat. Obzor. MR 1059547 | Zbl 0705.90053
[7] H. Samelson R. Thrall O. Wesler: A Partition Theorem for Euclidean n-Space. Proc. of the Amer. Math. Society 9 (1958), 805-807. MR 0097025
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