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)



The additive inverse eigenvalue problem and topological degree

Author: J. C. Alexander
Journal: Proc. Amer. Math. Soc. 70 (1978), 5-7
MSC: Primary 55M25; Secondary 15A18
MathSciNet review: 487546
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A short proof using topological degree is given of the additive inverse eigenvalue problem: The diagonal elements of any square complex matrix can be altered so as to cause the altered matrix to have any prescribed set of eigenvalues.

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

  • [1] S.-N. Chow, J. Mallet-Paret and J. A. Yorke, Finding zeroes of maps: homotopy methods that are constructive with probability one (preprint). MR 492046 (80d:55002)
  • [2] S. Friedland, Matrices with prescribed off-diagonal elements, Israel J. Math. 11 (1972), 184-189. MR 0379526 (52:431)
  • [3] -, On inverse multiplicative eigenvalue problems for matrices, Linear Algebra and Appl. 12 (1975), 127-137. MR 0432672 (55:5658)
  • [4] -, Inverse eigenvalue problems (preprint).
  • [5] R. B. Kellogg, T. Y. Li and J. A. Yorke, A method of continuation for calculating a Brouwer fixed point, Fixed Points, Algorithms and Applications, S. Karamadian (editor), Academic Press, New York, 1977.
  • [6] -, A constructive proof of the Brouwer Fixed Point Theorem and computational results, SIAM J. Numer. Anal. 13 (1976), 473-483. MR 0416010 (54:4087)
  • [7] J. W. Milnor, Topology from the differential viewpoint, Univ. of Virginia Press, Charlottesville, Va., 1965. MR 0226651 (37:2239)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55M25, 15A18

Retrieve articles in all journals with MSC: 55M25, 15A18

Additional Information

Article copyright: © Copyright 1978 American Mathematical Society

American Mathematical Society