Totally positive matrices. (English. Russian original) Zbl 0331.15012
Sib. Math. J. 16(1975), 636-641 (1976); translation from Sib. Mat. Zh. 16, 830-836 (1975).
MSC:
| 15B48 | Positive matrices and their generalizations; cones of matrices |
| 15A18 | Eigenvalues, singular values, and eigenvectors |
| 65F15 | Numerical computation of eigenvalues and eigenvectors of matrices |
References:
| [1] | M. G. Krein and M. A. Rutman, ?Linear operators which leave a cone in a Banach space invariant,? Usp. Mat. Nauk,3, No. 1, 3-95 (1948). · Zbl 0030.12902 |
| [2] | M. A. Krasnosel’skii, Positive Solutions of Operator Equations [in Russian], Fizmatgiz, Moscow (1962). |
| [3] | P. P. Zabreiko, M. A. Krasnosel’skii, and Yu. V. Pokornyi, ?A certain class of linear positive operators,? Funktsional. Analiz i Ego Prilozhen.,5, No. 4, 9-17 (1971). · Zbl 0237.34098 · doi:10.1007/BF01075842 |
| [4] | M. A. Krasnosel’skii, G. M. Vainikko, P. P. Zabreiko, Ya. B. Rutitskii, and V. Ya. Stetsenko, Approximate Solution of Operator Equations [in Russian], Fizmatgiz, Moscow (1969). |
| [5] | F. R. Gantmakher and M. G. Krein, Oscillatory Matrices and Small Oscillations of Mechanical Systems [in Russian], Gostekhizdat, Moscow-Leningrad (1950). |
| [6] | I. J. Schoenberg, ?Über variationvermindernde lineare transformationen,? Math. Z.,32, 321-328 (1930). · JFM 56.0106.06 · doi:10.1007/BF01194637 |
| [7] | F. Hausdorff, Set Theory, 2nd ed., Chelsea, New York (1962). · Zbl 0060.12401 |
| [8] | B. N. Sadovskii, ?Operators which are compact in the limit and condensing,? Usp. Mat. Nauk,27, No. 1 (163), 81-146 (1972). |
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