کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6416143 | 1631101 | 2016 | 18 صفحه PDF | دانلود رایگان |
In this paper, we describe the eigenstructure and the Jordan form of the Fourier transform matrix generated by a primitive N-th root of unity in a field of characteristic 2. We find that the only eigenvalue is λ=1 and its eigenspace has dimension [N4]+1; we provide a basis of eigenvectors and a Jordan basis. The problem has already been solved, for number theoretic transforms, in any other finite characteristic. However, in characteristic 2 classical results about geometric multiplicity do not apply and we have to resort to different techniques in order to determine a basis of eigenvectors and a Jordan basis. We make use of a modified version of the Vandermonde's formula, which applies to matrices whose entries are powers of elements of the form x+xâ1.
Journal: Linear Algebra and its Applications - Volume 494, 1 April 2016, Pages 245-262