Equality in Wielandt’s eigenvalue inequality
Shmuel Friedland
Special Matrices, Tome 3 (2015), / Harvested from The Polish Digital Mathematics Library

In this paper we give necessary and sufficient conditions for the equality case in Wielandt’s eigenvalue inequality.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:269946
@article{bwmeta1.element.doi-10_1515_spma-2015-0005,
     author = {Shmuel Friedland},
     title = {Equality in Wielandt's eigenvalue inequality},
     journal = {Special Matrices},
     volume = {3},
     year = {2015},
     zbl = {1315.15017},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_spma-2015-0005}
}
Shmuel Friedland. Equality in Wielandt’s eigenvalue inequality. Special Matrices, Tome 3 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_spma-2015-0005/

[1] K. Fan, On a theorem of Weyl concerning eigenvalues of linear transformations, I. Proc. Nat. Acad. Sci. U. S. A. 35 (1949), 652–655. [Crossref]

[2] S. Friedland, Extremal eigenvalue problems, Bull. Brazilian Math. Soc. 9 (1978), 13-40. | Zbl 0441.47024

[3] S. Friedland, A generalization of the Motzkin-Taussky theorem, Linear Algebra Appl. 36 (1981), 103-109. [Crossref] | Zbl 0452.15003

[4] G.H. Hardy, J.E. Littlewood and G. Pólya, Inequalities, Cambridge Univ. Press, Second edition, 1952.

[5] T. Kato, A Short Introduction to Perturbation Theory for Linear Operators, Springer-Verlag, 2nd ed., New York 1982. | Zbl 0493.47008

[6] V.B. Lidskii, On the characteristic numbers of the sum and product of symmetric matrices. Doklady Akad. Nauk SSSR (N.S.) 75, (1950) 769–772.

[7] N. Moiseyev and S. Friedland, The association of resonance states with incomplete spectrum of finite complex scaled Hamiltonian matrices, Phys. Rev. A 22 (1980), 619-624.

[8] F. Rellich, Perturbation Theory of Eigenvalue Problems, Gordon & Breach, New York, 1969.

[9] H. Wielandt, An extremum property of sums of eigenvalues, Proc. Amer. Math. Soc. 6 (1955), 106-110. [Crossref] | Zbl 0064.24703