Can One use mathematica or maple online? Is it possible to use some of these algebra packages online ?
I have some matrices that I would like to know the characteristic polynomial of.
Where could I send them to get a nicely factorised answer ?
My PC is very slow & it would be nice to use someone elses super powerful computer !
Any suggestions 

For Mathematica, you can try Wolfram Alpha:
factor the characteristic polynomial of [[0, 3], [1, 4]]

For Sage, you can try Sagenb.org.  There, you can do
import numpy
n=numpy.array([[0, 3],[1, 4]],'complex64')
m = matrix(n)
m.characteristic_polynomial().factor()

I'm not an expert on this in Sage, but the numpy appears to be necessary to get the polynomial to factor over the complex numbers.
Wolfram Alpha is going to be a lot more user friendly.  Notice I just typed in the description of what I wanted and I got it.  But, it's not as powerful because it's not a full fledged computer algebra system.  If you want to do several steps of calculations where you use a previous step in the next one, it's going to be very difficult or impossible.  But, with Sage, which can be used online for free, or you can download it for free, it will be more complicated to use but more powerful as well, overall.  So, it depends on what your needs are.
