Geodesic
On matrices having an invariant cone
Czechoslovak Mathematical Journal, Tome 22 (1972) no. 1, pp. 49-68

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
DOI : 10.21136/CMJ.1972.101076
Classification : 15A48 
Barker, George Phillip. On matrices having an invariant cone. Czechoslovak Mathematical Journal, Tome 22 (1972) no. 1, pp. 49-68. doi: 10.21136/CMJ.1972.101076
@article{10_21136_CMJ_1972_101076,
     author = {Barker, George Phillip},
     title = {On matrices having an invariant cone},
     journal = {Czechoslovak Mathematical Journal},
     pages = {49--68},
     year = {1972},
     volume = {22},
     number = {1},
     doi = {10.21136/CMJ.1972.101076},
     mrnumber = {0302672},
     zbl = {0238.15005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1972.101076/}
}
TY  - JOUR
AU  - Barker, George Phillip
TI  - On matrices having an invariant cone
JO  - Czechoslovak Mathematical Journal
PY  - 1972
SP  - 49
EP  - 68
VL  - 22
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1972.101076/
DO  - 10.21136/CMJ.1972.101076
LA  - en
ID  - 10_21136_CMJ_1972_101076
ER  - 
%0 Journal Article
%A Barker, George Phillip
%T On matrices having an invariant cone
%J Czechoslovak Mathematical Journal
%D 1972
%P 49-68
%V 22
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1972.101076/
%R 10.21136/CMJ.1972.101076
%G en
%F 10_21136_CMJ_1972_101076

[1] Birkhoff G.: Linear transformations with invariant cones. American Math. Monthly. 74, 114-216 (1967). | DOI | MR | Zbl

[2] Drazin M. P. J. W. Dungey, K. W. Gruenherg: Some theorems on commutative matrices. J. London Math. Soc. 26, 221-228 (1951). | MR

[3] Fan K.: Inequahties for M-matrices. Indag. Math. 26, 602-610 (1964). | DOI | MR

[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

[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

[6] Householder A. S.: On matrices with nonnegative elements. Monatsh. Math. 62, 238-242 (1958). | DOI | MR

[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

[8] Krasnoselskii M A.: Positive Solutions of Operator Equations. Groningen: P. Noordhoff, Ltd. 1964. | MR

[9] Mangasarian O. L.: A convergent splitting of matrices. MRC Tech. Rep. #958 (1969). | MR

[10] Marek I.: Spektrale Eigenschaften der K-positiven Operatoren und Einschliessungssätze für den Spektralradius. Czech. Math. J. 16, 493-517 (1966). | MR | Zbl

[11] Marek I.: $u_0$-positive operators and some of their applications. SIAM J. Appl. Math. 15, 484-494 (1967). | DOI | MR

[12] Pták V,: On a combinatorial theorem and its application to nonnegative matrices. Czech. Math. J. 8, 487-495 (1958). (In Russian.) | MR

[13] Sawashima L: On spectral properties of some positive operators. Nat. Sci. Rep. of the Ochanormizu University. 75, 53-64 (1964). | MR | Zbl

[14] Schneider H.: Positive operators and an inertia theorem. Numerische Math. 7, 11-17 (1965). | DOI | MR | Zbl

[15] Stetsenko V. Ja.: Критерии нерозложимости линейных операторов. UMN. 21 (131), 265-267 (1966). | Zbl

[16] Vandergraft J. S.: Spectral properties of matrices which have invariant cones. SIAM J. Appl. Math. 16, 1208-1222 (1968). | DOI | MR | Zbl

[17] Varga R. S.: Matrix Iterative Analysis. Englewood Cliffs: Prentice-Hall, Inc. 1962. | MR

[18] Wielandt H.: Topics in the Analytic Theory of Matrices (Lecture Notes). University of Wisconsin: Department of Mathematics. Madison, 1967.

Cité par Sources :