crounse@norton.uucp (Great Rumpuscat) (06/29/91)
A paper* I was just reading presents the following definition and result: A ``circulant'' is a matrix which has the same set of elements rotated by one position in each subsequent row, e.g., / 1 2 3 4 \ | 4 1 2 3 | | 3 4 1 2 | \ 2 3 4 1 / A matrix which is a ``circulant'' has eigenvalues which are, to a constant, the Inverse Discrete Fourier Transform of the row elements. In the paper, this result is presented without reference. This fact seems quite amazing (to me), and I would expect that it must be widely known in the proper circles. If so, would someone please tell me where I could find a book or article which discusses such matrices? Thanks, Ken Crounse * "Stability in Contractive Nonlinear Neural Networks," Douglas G. Kelly IEEE TrBioMedEng March 1990 ,,,,,,,,,,,,,,,,,crounse@norton.berkeley.edu,,,,,,,,,,,,,,,,,,,,,,, Kenneth R. Crounse, - UC Berkeley King of - (Rally Behind the Ridiculous) Randomness and - Dept. of EECS Chaos - Nonlinear Electronics Laboratory