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On Joint Eigenvalues of Commuting Matrices

Published online by Cambridge University Press:  20 November 2018

R. Bhatia  and
L. Elsner
R. Bhatia
Affiliation:
Indian Statistical Institute, Delhi centre, 7. SJS Sansanwal Marg, New Delhi 110016, India
L. Elsner
Affiliation:
Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany
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Abstract

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A spectral radius formula for commuting tuples of operators has been proved in recent years. We obtain an analog for all the joint eigenvalues of a commuting tuple of matrices. For a single matrix this reduces to an old result of Yamamoto.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 2 , 01 June 1996 , pp. 164 - 168
Copyright
Copyright © Canadian Mathematical Society 1996

References

1. Bhatia, R. and Bhattacharyya, T., On the joint spectral radius of commuting matrices, Studia Math. 114 (1995), 29–38.Google Scholar
2. Cho, M. and Huruya, T., On the joint spectral radius, Proc. Roy. Irish Acad. Sect. A 91(1991), 39–44.Google Scholar
3. Gantmacher, F. R., The Theory of Matrices, Chelsea, 1977.Google Scholar
4. Marcus, M. and Mine, H., A Survey of Matrix Theory and Matrix inequalities, Prindle, Weber and Schmidt, Boston, 1964.Google Scholar
5. Müller, V. and Solrysiak, A., Spectral radius formula for commuting Hilbert space operators, Studia Math., 103(1992), 329–333.Google Scholar
6. Yamamoto, T., On the extreme values of the roots of matrices, J. Math. Soc. Japan 19(1967), 173–178.Google Scholar