2012-02-12T00:39:52Z http://techrept.petermmaurer.com/comments/atom.aspx Quick Blogcast tag:techrept.petermmaurer.com,2007-02-04:244339 Peter M. Maurer 2007-02-05T03:51:43Z 2007-02-05T03:51:43Z Sometimes it pays to take look back at the book before exerting a lot of effort. If p is any irreducible polynomial of degree m over GF(2), and a is any root of p, then GF(2^m) has basis vectors 1, a, a^2, ... , a^m-1. Furthermore, the complete list of roots of p is a, a^2, a^4, a^8, ... a^2^i, a^2^m-1. Thus, for every irreducible polynomial p over GF(2) a being a root of p also implies that a^2 is a root of p. Since the roots of p are mathematically indistinguishable, every square of every eigenvalue of a GF(2) matrix is also an eigenvalue of the same matrix.