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Eigenvalues of matrices with prescribed entries


Authors: David London and Henryk Minc
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
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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$.


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

  • [1] H. K. Farahat and W. Ledermann, Matrices with prescribed characteristic polynomials, Proc. Edinburgh Math. Soc. 11 (1958/59), 143-146. MR 21 #6382. MR 0107659 (21:6382)
  • [2] M. Marcus and H. Minc, A survey of matrix theory and matrix inequalities, Allyn and Bacon, Boston, Mass., 1964. MR 29 #112. MR 0162808 (29:112)
  • [3] L. Mirsky, Matrices with prescribed characteristic roots and diagonal elements, J. London Math. Soc. 33 (1958), 14-21. MR 19, 1034. MR 0091931 (19:1034c)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0352125-X
Keywords: Eigenvalues, matrices, prescribed entries, prescribed eigenvalues, simple eigenvalues
Article copyright: © Copyright 1972 American Mathematical Society

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