Recent content by geor

Okay, so this is a similar way that seems to work for me: Suppose F_{p^n}=F_p(a), where a is a root of some irreducible polynomial over F_p of degree n. Then, a^(p^n-1), ..., a^{p^2}, a^p, a (= a^{p^n}) is a basis of the F_p-vector space F_p(a) Then we notice that \phi(a^{p^i}) = a^{p^i+1}...

Hello all, I am trying to solve this exercise here: Let \phi denote the Frobenius map x |-> x^p on the finite field F_{p^n}. Determine the Jordan canonical form (over a field containing all the eigenvalues) for \phi considered as an F_p-linear transformation of the n-dimensional F_p-vector...

Thanks a lot for the feedback! I see it now..

Hello all, In wikipedia, http://en.wikipedia.org/wiki/Rank%E2%80%93nullity_theorem" a generalized rank-nulity theorem as below: "If V, W are vector spaces and T : V -> W is a linear operator then V is isomorphic with the direct sum of im(T) and ker(T)". I had an exercise in Algebra which...

Thanks a lot!

Ooops! I think I see it now.. They are isomorphic as vector spaces but not as fields, right? The isomorphism I said above does not respect the product.. That's it, right?!

Hello all, I am studying Algebra and in the chapter where Galois theory is introduced, I see the following exercise: "Prove that Q(sqrt(2)) and Q(sqrt(3)) are not isomorphic" Well, It seems that I am a bit behind because I really don't get it... :( I mean, I'm sure that this is the case...

Oh yes, of course! Thanks a lot..

Hello all, I am aware that we can write ln(x) as a series. But what can we say for a logarithm of an arbitrary base? Can we write for example log_2(x) as series? Thanks in advance..

Oh yes, I see it now! Thanks so much!

Hello everybody, I have a question for which I cannot find the answer around, any help would be really appreciated. Suppose we have a matrix A of a linear transformation of a vector space, with only one eigenvalue, say 's'. My question is: Is the operator (A-sI) nilpotent? ('I' is the...

What a nice tool! I was struggling for so much time trying to change that variables!

Thanks so much for the help!

It is possible, is it not?!

Thanks for taking the time to answer! Well, no, I started from there, I want to write this as a polynomial of x in the usual way, that is, in the form: a_n*x^n+...+a_1*x+a_0 I want to have only x there...