Equality in Wielandt’s eigenvalue inequality

Shmuel Friedland

Special Matrices (2015)

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

Abstract

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

How to cite

top

Shmuel 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. [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. [2] S. Friedland, Extremal eigenvalue problems, Bull. Brazilian Math. Soc. 9 (1978), 13-40. Zbl0441.47024
  3. [3] S. Friedland, A generalization of the Motzkin-Taussky theorem, Linear Algebra Appl. 36 (1981), 103-109. [Crossref] Zbl0452.15003
  4. [4] G.H. Hardy, J.E. Littlewood and G. Pólya, Inequalities, Cambridge Univ. Press, Second edition, 1952. 
  5. [5] T. Kato, A Short Introduction to Perturbation Theory for Linear Operators, Springer-Verlag, 2nd ed., New York 1982. Zbl0493.47008
  6. [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. [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. [8] F. Rellich, Perturbation Theory of Eigenvalue Problems, Gordon & Breach, New York, 1969. 
  9. [9] H. Wielandt, An extremum property of sums of eigenvalues, Proc. Amer. Math. Soc. 6 (1955), 106-110. [Crossref] Zbl0064.24703

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.