Normal Toeplitz Matrices
نویسندگان
چکیده
It is well-known from the work of A. Brown and P.R. Halmos that an infinite Toeplitz matrix is normal if and only if it is a rotation and translation of a Hermitian Toeplitz matrix. In the present article we prove that all finite normal Toeplitz matrices are either generalised circulants or are obtained from Hermitian Toeplitz matrices by rotation and translation. ∗Supported in part by an NSERC Research Grant †Postdoctoral Fellow, supported in part by grants from NSERC ‡Supported in part by KOSEF Project No. 94-0701-02-01-3 and GARC-KOSEF (1995)
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It would be correct to add that the main contribution of [2] was to prove, for arbitrary n, the necessity of some equalities for the entries of a normal Toeplitz matrix of order n. These equalities are in fact equivalent to the authors’ equations (1) in the real case. The full solution of the problem (of describing normal Toeplitz matrices) for the real case was given in [3]. The same year anot...
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عنوان ژورنال:
- SIAM J. Matrix Analysis Applications
دوره 17 شماره
صفحات -
تاریخ انتشار 1996