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Journal of the American Mathematical Society

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ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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The inverse eigenvalue problem for real symmetric Toeplitz matrices
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by H. J. Landau PDF
J. Amer. Math. Soc. 7 (1994), 749-767 Request permission


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.
    N. I. Akhiezer, The classical moment problem, Hafner, New York, 1965. M. Berger and M. Berger, Perspectives in nonlinearity, Benjamin, New York, 1968.
  • P. Delsarte and Y. Genin, Spectral properties of finite Toeplitz matrices, Mathematical theory of networks and systems (Beer Sheva, 1983) Lect. Notes Control Inf. Sci., vol. 58, Springer, London, 1984, pp. 194–213. MR 792106, DOI 10.1007/BFb0031053
  • Shmuel Friedland, Inverse eigenvalue problems for symmetric Toeplitz matrices, SIAM J. Matrix Anal. Appl. 13 (1992), no. 4, 1142–1153. MR 1182718, DOI 10.1137/0613069
  • I. S. Iohvidov, Hankel and Toeplitz matrices and forms, Birkhäuser, Boston, Mass., 1982. Algebraic theory; Translated from the Russian by G. Philip A. Thijsse; With an introduction by I. Gohberg. MR 677503
  • T. Kato, Perturbation theory for linear operators, Springer, New York, 1984. F. Riesz and B. Sz-Nagy, Functional analysis, Ungar, New York, 1971.
  • J. T. Schwartz, Nonlinear functional analysis, Notes on Mathematics and its Applications, Gordon and Breach Science Publishers, New York-London-Paris, 1969. Notes by H. Fattorini, R. Nirenberg and H. Porta, with an additional chapter by Hermann Karcher. MR 0433481
  • David Slepian and Henry J. Landau, A note on the eigenvalues of Hermitian matrices, SIAM J. Math. Anal. 9 (1978), no. 2, 291–297. MR 466171, DOI 10.1137/0509020
  • William F. Trench, Spectral evolution of a one-parameter extension of a real symmetric Toeplitz matrix, SIAM J. Matrix Anal. Appl. 11 (1990), no. 4, 601–611. MR 1066162, DOI 10.1137/0611043
  • William F. Trench, Interlacement of the even and odd spectra of real symmetric Toeplitz matrices, Linear Algebra Appl. 195 (1993), 59–68. MR 1253269, DOI 10.1016/0024-3795(93)90256-N
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 7 (1994), 749-767
  • MSC: Primary 15A18; Secondary 15A21, 15A60, 47B35
  • DOI:
  • MathSciNet review: 1234570