Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Upper and lower bounds of eigenvalues: Mode-clamping theorems

Author: M. Sparks
Journal: Quart. Appl. Math. 28 (1970), 103-109
MSC: Primary 65.40
DOI: https://doi.org/10.1090/qam/264842
MathSciNet review: 264842
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Upper and lower bounds for the eigenvalues of three types of matrices $ M$ are established. If $ M$ is written as the sum of a diagonal matrix $ D$ plus a matrix $ A$, the real parts of the eigenvalues of $ M$ must lie between the real parts of the neighboring diagonal elements of $ D$, no matter how large the elements of $ A$ or how closely spaced the diagonal elements of $ D$.

References [Enhancements On Off] (What's this?)

  • [1] M. Sparks (to be published)
  • [2] L. Schiff, Quantum mechanics, McGraw-Hill, New York, 1955
  • [3] J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965. MR 0184422
  • [4] M. Sparks, Green's functions; state vector approach for physicists (to be published)
  • [5] A. M. Clogston, H. Suhl, L. R. Walker and P. W. Anderson, J. Phys. Chem. Solids 1, 129 (1956)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 65.40

Retrieve articles in all journals with MSC: 65.40

Additional Information

DOI: https://doi.org/10.1090/qam/264842
Article copyright: © Copyright 1970 American Mathematical Society

American Mathematical Society