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 $2n - 2$.References
- H. K. Farahat and W. Ledermann, Matrices with prescribed characteristic polynomials, Proc. Edinburgh Math. Soc. 11 (1958/1959), 143–146. MR 0107659, DOI 10.1017/s0013091500021611
- Marvin Marcus and Henryk Minc, A survey of matrix theory and matrix inequalities, Allyn and Bacon, Inc., Boston, Mass., 1964. MR 0162808
- L. Mirsky, Matrices with prescribed characteristic roots and diagonal elements, J. London Math. Soc. 33 (1958), 14–21. MR 91931, DOI 10.1112/jlms/s1-33.1.14
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