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...
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...
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...
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..
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...
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...