Equality in Wielandt’s eigenvalue inequality

• Autorzy: Shmuel Friedland
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

Lidski’s theorem; Wielandt’s eigenvalue inequality

Kategorie tematyczne

• 15A22: Matrix pencils
• 15A18: Eigenvalues, singular values, and eigenvectors
• 15B57: Hermitian, skew-Hermitian, and related matrices

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2015-01-15

zaakceptowano

2015-03-22

online

2015-04-09

Twórcy

autor

Shmuel Friedland

• Department of Mathematics, Statistics and Computer Science, University of
  Illinois at Chicago, Chicago, Illinois 60607-7045, USA

Bibliografia

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

Identyfikatory

DOI

10.1515/spma-2015-0005