Re: Toeplitz Matrix, DFT, and rank


<bergers@xxxxxxx> wrote in message
news:1128051258.865208.42050@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> Hello All,
>
> I recall reading a paper that stated that an N X N conjugate symmetric
> (Hermitian) Toeplitz matrix is nonsingular if none of elements of the
> discrete Fourier transform of the first row equal zero. I can't find
> the paper in my files, can some one provide a reference? Also
> interested in knowing if the rank of the matrix can be determine by the
> number of non-zero elements of the discrete Fourier transform of the
> first row.

This is certainly true for a cyclic matrix, which is special Toeplitz, since
the eigenvalues are the DFT coefficients.

rusty





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