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

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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.

**[1]**Shui Nee Chow, John Mallet-Paret, and James A. Yorke,*Finding zeroes of maps: homotopy methods that are constructive with probability one*, Math. Comp.**32**(1978), no. 143, 887–899. MR**492046**, 10.1090/S0025-5718-1978-0492046-9**[2]**Shmuel Friedland,*Matrices with prescribed off-diagonal elements*, Israel J. Math.**11**(1972), 184–189. MR**0379526****[3]**Shmuel Friedland,*On inverse multiplicative eigenvalue problems for matrices*, Linear Algebra and Appl.**12**(1975), no. 2, 127–137. MR**0432672****[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]**R. B. Kellogg, T. Y. Li, and J. Yorke,*A constructive proof of the Brouwer fixed-point theorem and computational results*, SIAM J. Numer. Anal.**13**(1976), no. 4, 473–483. MR**0416010****[7]**John W. Milnor,*Topology from the differentiable viewpoint*, Based on notes by David W. Weaver, The University Press of Virginia, Charlottesville, Va., 1965. MR**0226651**

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1978-0487546-3

Article copyright:
© Copyright 1978
American Mathematical Society