# Equality in Wielandt’s eigenvalue inequality

Special Matrices (2015)

- Volume: 3, Issue: 1, page 53-57, electronic only
- ISSN: 2300-7451

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topShmuel Friedland. "Equality in Wielandt’s eigenvalue inequality." Special Matrices 3.1 (2015): 53-57, electronic only. <http://eudml.org/doc/269946>.

@article{ShmuelFriedland2015,

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

author = {Shmuel Friedland},

journal = {Special Matrices},

keywords = {Lidski’s theorem; Wielandt’s eigenvalue inequality; Lidski's theorem; Wielandt's eigenvalue inequality; equality case},

language = {eng},

number = {1},

pages = {53-57, electronic only},

title = {Equality in Wielandt’s eigenvalue inequality},

url = {http://eudml.org/doc/269946},

volume = {3},

year = {2015},

}

TY - JOUR

AU - Shmuel Friedland

TI - Equality in Wielandt’s eigenvalue inequality

JO - Special Matrices

PY - 2015

VL - 3

IS - 1

SP - 53

EP - 57, electronic only

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

LA - eng

KW - Lidski’s theorem; Wielandt’s eigenvalue inequality; Lidski's theorem; Wielandt's eigenvalue inequality; equality case

UR - http://eudml.org/doc/269946

ER -

## References

top- [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. Zbl0441.47024
- [3] S. Friedland, A generalization of the Motzkin-Taussky theorem, Linear Algebra Appl. 36 (1981), 103-109. [Crossref] Zbl0452.15003
- [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. Zbl0493.47008
- [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] Zbl0064.24703

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