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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Eigenvalues of matrices with prescribed entries
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by David London and Henryk Minc PDF
Proc. Amer. Math. Soc. 34 (1972), 8-14 Request permission

Abstract:

It is shown that there exists an n-square matrix all whose eigenvalues and $n - 1$ of whose entries are arbitrarily prescribed. This result generalizes a theorem of L. Mirsky. It is also shown that there exists an n-square matrix with some of its entries prescribed and with simple eigenvalues, provided that n of the nonprescribed entries lie on a diagonal or, alternatively, provided that the number of prescribed entries does not exceed $2n - 2$.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 34 (1972), 8-14
  • MSC: Primary 15A18
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0352125-X
  • MathSciNet review: 0352125