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Eigenvalues of complex tridiagonal matrices

Published online by Cambridge University Press:  20 January 2009

P. M. Gibson
P. M. Gibson
Affiliation:
University of Alabama in Huntsville, Huntsville, Alabama 35807, U.S.A.
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Results of Arscott (1) and Jayne (3) on real matrices are generalized to obtain bounds for the real parts of the eigenvalues of certain complex tridiagonal matrices, and bounds for the imaginary parts of the eigenvalues of other tridiagonal matrices are given. It is shown that analogous results hold for zeros of the permanent of certain characteristic matrices.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 17 , Issue 4 , December 1971 , pp. 317 - 319
Copyright
Copyright © Edinburgh Mathematical Society 1971

References

REFERENCES

(1) Arscott, F. M., Latent roots of tri-diagonal matrices, Edinburgh Math. Notes 44, 5–7CrossRefGoogle Scholar
[in Proc. Edinburgh Math. Soc. (2) 12 (1961)].Google Scholar
(2) Gibson, P. M., An identity between permanents and determinants, Amer. Math. Monthly 76 (1969), 270–271.CrossRefGoogle Scholar
(3) Jayne, J. W., An exclusion theorem for tri-diagonal matrices, Proc. Edinburgh Math. Soc. (2) 16 (1969), 251–253.CrossRefGoogle Scholar
(4) Marcus, M. and Minc, H., A Survey of Matrix Theory and Matrix Inequalities (Allyn and Bacon, Boston, 1964).Google Scholar