| Title:
|
On matrices having an invariant cone (English) |
| Author:
|
Barker, George Phillip |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
22 |
| Issue:
|
1 |
| Year:
|
1972 |
| Pages:
|
49-68 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| MSC:
|
15A48 |
| idZBL:
|
Zbl 0238.15005 |
| idMR:
|
MR0302672 |
| DOI:
|
10.21136/CMJ.1972.101076 |
| . |
| Date available:
|
2008-06-09T13:55:09Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/101076 |
| . |
| Reference:
|
[1] Birkhoff G.: Linear transformations with invariant cones.American Math. Monthly. 74, 114-216 (1967). Zbl 0192.26703, MR 0214605, 10.2307/2316020 |
| Reference:
|
[2] Drazin M. P. J. W. Dungey, K. W. Gruenherg: Some theorems on commutative matrices.J. London Math. Soc. 26, 221-228 (1951). MR 0041095 |
| Reference:
|
[3] Fan K.: Inequahties for M-matrices.Indag. Math. 26, 602-610 (1964). MR 0170898, 10.1016/S1385-7258(64)50067-0 |
| Reference:
|
[4] Fiedler M., and V. Pták: On matrices with non-positive off-diagonal elements and positive principal minors.Czech. Math. J. 12, 382-400 (1962). MR 0142565 |
| Reference:
|
[5] Fiedler M., and V. Pták: Some results on matrices of class K and their application to the convergence of iteration procedures.Czech. Math. J. 16, 260-273 (1966). MR 0196898 |
| Reference:
|
[6] Householder A. S.: On matrices with nonnegative elements.Monatsh. Math. 62, 238-242 (1958). MR 0095857, 10.1007/BF01303968 |
| Reference:
|
[7] Krein M. G., and M. A. Rutman: Linear operators leaving invariant a cone in a Banach space.. American Math. Soc. Translations Ser. I, 10, 199-325 (1962) (originally Uspehi Mat. Nauk (N.S.) 3, 3--95 (1948)). MR 0027128 |
| Reference:
|
[8] Krasnoselskii M A.: Positive Solutions of Operator Equations.Groningen: P. Noordhoff, Ltd. 1964. MR 0181881 |
| Reference:
|
[9] Mangasarian O. L.: A convergent splitting of matrices.MRC Tech. Rep. #958 (1969). MR 0266409 |
| Reference:
|
[10] Marek I.: Spektrale Eigenschaften der K-positiven Operatoren und Einschliessungssätze für den Spektralradius.Czech. Math. J. 16, 493-517 (1966). Zbl 0152.33701, MR 0217622 |
| Reference:
|
[11] Marek I.: $u_0$-positive operators and some of their applications.SIAM J. Appl. Math. 15, 484-494 (1967). MR 0233176, 10.1137/0115044 |
| Reference:
|
[12] Pták V,: On a combinatorial theorem and its application to nonnegative matrices.Czech. Math. J. 8, 487-495 (1958). (In Russian.) MR 0110644 |
| Reference:
|
[13] Sawashima L: On spectral properties of some positive operators.Nat. Sci. Rep. of the Ochanormizu University. 75, 53-64 (1964). Zbl 0138.07801, MR 0187096 |
| Reference:
|
[14] Schneider H.: Positive operators and an inertia theorem.Numerische Math. 7, 11-17 (1965). Zbl 0158.28003, MR 0173678, 10.1007/BF01397969 |
| Reference:
|
[15] Stetsenko V. Ja.: Критерии нерозложимости линейных операторов.UMN. 21 (131), 265-267 (1966). Zbl 0178.50202 |
| Reference:
|
[16] Vandergraft J. S.: Spectral properties of matrices which have invariant cones.SIAM J. Appl. Math. 16, 1208-1222 (1968). Zbl 0186.05701, MR 0244284, 10.1137/0116101 |
| Reference:
|
[17] Varga R. S.: Matrix Iterative Analysis.Englewood Cliffs: Prentice-Hall, Inc. 1962. MR 0158502 |
| Reference:
|
[18] Wielandt H.: Topics in the Analytic Theory of Matrices (Lecture Notes).University of Wisconsin: Department of Mathematics. Madison, 1967. |
| . |
