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 Apr 21 revised How can I construct the matrix representing a linear transformation of a 2x2 matrix to its transpose with respect to a given set of bases? Added comments about the choice of basis and its order Mar 16 comment Finite field question involving the trace and a permutation. Many thanks Jyrki, I'll need to study this a bit. I'll update later. Mar 16 revised Finite field question involving the trace and a permutation. added 364 characters in body Mar 16 comment Finite field question involving the trace and a permutation. I know a couple of people who were claiming that they could do math better after a couple of beers :) Anyway, I think I have an idea, but I have to double think before posting anything, I'm not sure yet. Mar 10 revised Finite field question involving the trace and a permutation. added 31 characters in body Mar 10 comment Bijections of a finite field that preserve the kernel of the trace I have realized what my $f(x)$ should be. Indeed, I was asking too much. If you want, check my updated question here: math.stackexchange.com/questions/1183155/… Mar 10 asked Finite field question involving the trace and a permutation. Feb 24 comment Bijections of a finite field that preserve the kernel of the trace Thank you for your clear and thorough answer, I was quite off with my conjecture about these monomials. I will have to think how/if the question can be restated to suggest some other class of polynomials. Feb 24 comment Bijections of a finite field that preserve the kernel of the trace I think I was being quite careless when I wrote that title. It should be just bijections. Feb 24 revised Bijections of a finite field that preserve the kernel of the trace Changed the title as per my answer to a comment Feb 24 accepted Bijections of a finite field that preserve the kernel of the trace Feb 23 asked Bijections of a finite field that preserve the kernel of the trace Jan 22 asked Is LU decomposition of matrices efficient for today's standards? Jan 20 accepted Intersection of blocks of the symmetric BIBD $PG(d,q)$ Jul 9 accepted Which powers of a primitive element of a finite field yield a generator of a finite field extension? Jul 7 comment Which powers of a primitive element of a finite field yield a generator of a finite field extension? Thanks for your answer. Now, you say that WLOG, $i|(q^m-1)$, else $i$ is associate to a divisor's residue in $\Bbb{Z}_{q^m-1}$. Could you comment on that? I fail to understand it.. Jul 4 comment Which powers of a primitive element of a finite field yield a generator of a finite field extension? Note that the last bullet is equivalent to "there is no $s$ such that \$0