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
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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 $D$.
M. Sparks (to be published)
L. Schiff, Quantum mechanics, McGraw-Hill, New York, 1955
- J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965. MR 0184422
M. Sparks, Green’s functions; state vector approach for physicists (to be published)
A. M. Clogston, H. Suhl, L. R. Walker and P. W. Anderson, J. Phys. Chem. Solids 1, 129 (1956)
M. Sparks (to be published)
L. Schiff, Quantum mechanics, McGraw-Hill, New York, 1955
J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965, pp. 84–96.
M. Sparks, Green’s functions; state vector approach for physicists (to be published)
A. M. Clogston, H. Suhl, L. R. Walker and P. W. Anderson, J. Phys. Chem. Solids 1, 129 (1956)
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Article copyright:
© Copyright 1970
American Mathematical Society
