Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A Henrici theorem for joint spectra of commuting matrices


Authors: Rajendra Bhatia and Tirthankar Bhattacharyya
Journal: Proc. Amer. Math. Soc. 118 (1993), 5-14
MSC: Primary 15A42; Secondary 15A66, 47A13
DOI: https://doi.org/10.1090/S0002-9939-1993-1160292-7
MathSciNet review: 1160292
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A version of Henrici's classical perturbation theorem for eigenvalues of matrices is obtained for joint spectra of commuting tuples of matrices. The approach involves Clifford algebra techniques introduced by McIntosh and Pryde.


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

  • [1] E. Artin, Geometric algebra, Wiley Interscience, New York, 1957. MR 0082463 (18:553e)
  • [2] F. L. Bauer and C. T. Fike, Norms and exclusion theorems, Numer. Math. 2 (1960), 137-141. MR 0118729 (22:9500)
  • [3] R. Bhatia, Perturbation bounds for matrix eigenvalues, Longman Scientific and Technical, Essex, England, 1987. MR 925418 (88k:15020)
  • [4] R. Bhatia, Ch. Davis, and A. McIntosh, Perturbations of spectral subspaces and solutions of linear operator equations, Linear Algebra Appl. 52 (1983), 45-67. MR 709344 (85a:47020)
  • [5] R. Bhatia and S. Friedland, Variation of Grassman powers and spectra, Linear Algebra Appl. 40 (1981), 1-18. MR 629603 (83b:15022)
  • [6] Ch. Davis, Perturbation of spectrum of normal operators and of commuting tuples, Linear and Complex Analysis Problem Book (V. P. Havin, S. V. Hruschev, and N. K. Nikol'ski, eds.), Lecture Notes in Math., vol. 1043, Springer, Berlin and New York, 1984.
  • [7] L. Elsner, On the variation of spectra of matrices, Linear Algebra Appl. 47 (1982), 127-138. MR 672736 (84h:15019)
  • [8] P. Henrici, Bounds for iterates, inverses, spectral variation and fields of values of non-normal matrices, Numer. Math. 4 (1962), 24-39. MR 0135706 (24:B1751)
  • [9] R. A. Horn and C. R. Johnson, Matrix analysis, Cambridge Univ. Press, Cambridge, 1985. MR 832183 (87e:15001)
  • [10] A. McIntosh and A. Pryde, A functional calculus for several commuting operators, Indiana Univ. Math. J. 36 (1987), 421-439. MR 891783 (88i:47007)
  • [11] A. McIntosh, A. Pryde, and W. Ricker, Comparison of joint spectra for certain classes of commuting operators, Studia Math. 88 (1988), 23-36. MR 932003 (89e:47006)
  • [12] F. Ming, Garske's inequality for an $ n$-tuple of operators, Integral Equations Operator Theory 14 (1991), 787-793. MR 1127537 (92k:47012)
  • [13] A. Pryde, A Bauer-Fike theorem for the joint spectrum of commuting matrices, Linear Algebra Appl. 173 (1992), 221-230. MR 1170512 (93i:15034)
  • [14] -, Optimal matching of joint eigenvalues for normal matrices, Monash Univ. Analysis Paper 74, March 1991.
  • [15] G. W. Stewart and J. Sun, Matrix perturbation theory, Academic Press, New York, 1990. MR 1061154 (92a:65017)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 15A42, 15A66, 47A13

Retrieve articles in all journals with MSC: 15A42, 15A66, 47A13


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1160292-7
Keywords: Clifford algebras, commuting tuples of matrices, joint spectrum, spectral variation, Henrici's theorem, measure of nonnormality
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society