I'm having some trouble getting started with this, if someone could point me in the right direction that would awesome.
If T(A) = A^t (A-transpose) show that +1 and - 1 are the only eigenvalues of T.
I think that my problem is that I don't know how to symbolize the matrix of linear transformation for T, but perhaps there is another way to go about doing this problem.
T is a linear operation on matrices that maps a matrix into its transpose? I started to say "Think about the fact that and have the same main diagonal", but then it occured to me that A might not be a square matrix. Certainly, you can look at and which must be the same in both matrices.
Also, I the fact that A is a square matrix was actually part of the problem (T is a linear operator on ).
Sorry I did not include that in the original problem, I guess I have a bad habit of over looking that part of the problem because I don't really have any idea what's going on, therefore it doesn't really make any difference to me what vector space the transformations in.