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The inverse eigenvalue problem for real symmetric Toeplitz matrices


Author: H. J. Landau
Journal: J. Amer. Math. Soc. 7 (1994), 749-767
MSC: Primary 15A18; Secondary 15A21, 15A60, 47B35
DOI: https://doi.org/10.1090/S0894-0347-1994-1234570-6
MathSciNet review: 1234570
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Abstract: We show that every set of $ n$ real numbers is the set of eigenvalues of an $ n \times n$ real symmetric Toeplitz matrix; the matrix has a certain additional regularity. The argument--based on the topological degree--is nonconstructive.


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

  • [A] N. I. Akhiezer, The classical moment problem, Hafner, New York, 1965.
  • [B] M. Berger and M. Berger, Perspectives in nonlinearity, Benjamin, New York, 1968.
  • [DG] P. Delsarte and Y. Genin, Spectral properties of finite Toeplitz matrices, Lecture Notes in Control and Inform. Sci., vol. 58, Springer, New York, 1984, pp. 194-213 MR 792106 (86k:15003)
  • [F] S. Friedland, Inverse eigenvalue problems for symmetric Toeplitz matrices, SIAM J. Matrix Anal. Appl. 13 (1992), 1142-1153. MR 1182718 (93j:15009)
  • [I] I. S. Iohvidov, Hankel and Toeplitz matrices and forms, Birkhaüser, Boston, 1982. MR 677503 (83k:15021)
  • [K] T. Kato, Perturbation theory for linear operators, Springer, New York, 1984.
  • [RN] F. Riesz and B. Sz-Nagy, Functional analysis, Ungar, New York, 1971.
  • [S] J. T. Schwartz, Nonlinear functional analysis, Gordon and Breach, New York, 1969. MR 0433481 (55:6457)
  • [SL] D. Slepian and H. J. Landau, A note on the eigenvalues of Hermitian matrices, SIAM J. Math. Anal. 9 (1978), 291-297. MR 0466171 (57:6052)
  • [T1] W. F. Trench, Spectral evolution of a one-parameter extension of a real symmetric Toeplitz matrix, SIAM J. Matrix Anal. Appl. 11 (1990), 601-611. MR 1066162 (91f:15030)
  • [T2] -, Interlacement of the even and odd spectra of real symmetric Toeplitz matrices, Linear Algebra Appl. 195 (1993), 59-69. MR 1253269 (95a:15008)

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Additional Information

DOI: https://doi.org/10.1090/S0894-0347-1994-1234570-6
Keywords: Toeplitz matrices, inverse eigenvalue problem, regular Toeplitz matrix
Article copyright: © Copyright 1994 American Mathematical Society

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