Geodesic
A~generalization of Gershgorin's theorem
Izvestiya. Mathematics , Tome 23 (1984) no. 3, pp. 545-560.

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Estimates convenient for applicatins are obtained for the eigenvalues of complex matrices. Some applications in stability theory are indicated. The results are obtained by methods of convex analysis and the theory of nonnegative matrices. Bibliography: 24 titles. 
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V. N. Solov'ev. A~generalization of Gershgorin's theorem. Izvestiya. Mathematics , Tome 23 (1984) no. 3, pp. 545-560. http://geodesic.mathdoc.fr/item/IM2_1984_23_3_a7/

[1] Gershgorin S. A., “Über die Abgrenzung der Eigenwerte einer Matrix”, Izv. AN SSSR, otd. fiz.-mat. nauk, 1931, 749–754 | Zbl

[2] Parodi M., Lokalizatsiya kharakteristicheskikh chisel matrits i ee primeneniya, IL, M., 1960 | MR

[3] Markus M., Mink X., Obzor po teorii matrits i matrichnykh neravenstv, Nauka, M., 1972 | MR

[4] Gudkov V. V., “Ob odnom priznake neosobennosti matrits”, Latviiskii matematicheskii ezhegodnik, Zinatne, Riga, 1965, 385–390 | MR

[5] Varga R. S., “On recurring theorems on diagonal dominance”, Linear Algebra and Applications, 13:1,2 (1976), 1–9 | DOI | MR | Zbl

[6] Brualdi R. A., “Matrices, Eigenvalues and Directed Graphs”, Linear and Multilinear Algebra, 11:2 (1982), 143–165 | DOI | MR | Zbl

[7] Gantmakher F. R., Teoriya matrits, izd. 3-e, Nauka, M., 1967 | MR

[8] Shklyarskii D. O., Chentsov N. N., Yaglom I. M., Geometricheskie neravenstva i zadachi na maksimum i minimum, Nauka, M., 1970

[9] Price E. B., “Bounds for determinants with dominant principal diagonal”, Proc. Amer. Math. Soc., 2 (1951), 497–502 | DOI | MR | Zbl

[10] Bailey D., Crabtree D., “Bounds for determinants”, Linear Algebra and Appl., 2:3 (1969), 303–309 | DOI | MR | Zbl

[11] Kotelyanskii D. M., “Otsenki dlya opredelitelei matrits s preobladayuschei glavnoi diagonalyu”, Izv. AN SSSR, ser. matem., 20:1 (1956), 137–144 | MR | Zbl

[12] Rokafellar R., Vypuklyi analiz, Mir, M., 1973

[13] Lorch E. R., “Differentiable inequalities and the theory of convex bodies”, Trans. Amer. Math. Soc., 71 (1951), 243–266 | DOI | MR | Zbl

[14] Elster K.-H., Erdman D., “Über das Konvexitätsvehalten homogener Funktionen vom Grade I”, Wiss. Z. Techn. Hochsch. Ilmenau, 17:3 (1971), 71–82 | MR | Zbl

[15] Wang C.-L., “Convexity and Inequalities”, J. Math. Anal. Appl., 72 (1979), 355–361 | DOI | MR | Zbl

[16] Berman A., Plemmons R. J., Nonnegative Matrices in the Mathematical Sciences, Academic Press, N.Y., 1979 | MR | Zbl

[17] Ostrowski A., “Über die Determinanten mit überwiegender Hauptdiagonale”, Comm. Math. Helv., 10 (1937), 69–96 | DOI | MR | Zbl

[18] Kotelyanskii D. M., “O raspolozhenii tochek matrichnogo spektra”, Ukr. matem. zhurnal, 7:2 (1955), 131–133 | MR | Zbl

[19] Ostrowski A., “Über das Nichtverschwinden einer Klasse von Determinanten und die Lokalisierung der charakteristischen Wurzeln von Matrizen”, Compositio Math., 9:3 (1951), 209–226 | MR | Zbl

[20] Bekkenbakh E., Bellman R., Neravenstva, Mir, M., 1965 | MR

[21] Barbashin E. A., Funktsii Lyapunova, Nauka, M., 1970 | MR | Zbl

[22] Solovev V. N., “O kriterii vypuklosti polozhitelno odnorodnoi funktsii”, Matem. sbornik, 118:2 (1982), 280–286 | MR

[23] Berman A., Matrices and Mathematical Programming, Lecture Notes in Economics and Mathematical Systems, 79, Springer-Verlag, Berlin, 1973 | MR | Zbl

[24] Barker G. P., Carlson D., “Cones of diagonally dominant matrices”, Pacific. J. Math., 57:1 (1975), 15–32 | MR | Zbl