Abstract
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+x−1.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
