oh well i thought you were asking for something other than the OP o.o
intuitively...the transitive action takes one orbit to another orbit?
the orbit should be {g*x} for x in X
oh shoot. yes that's totally wrong lol...
if a = b, b = c, then a = c.
edit: could i be sending x to the whole set of X? could i send it to the whole thing or only one element of X? I'm not sure.
Homework Statement
A group G acts transitively on a non empty G-set S if, for all s1, s2 in S, there exists an element G in G such that g*s1 = s2. Characterize transitive G-set actions in terms of orbits. Prove your answer
Homework Equations
Transitive G-set Actions: for all s1, s2 in S...
Okay, so I have a few questions:
1) i think i could say that W is linearly dependent? since \lambda1 + \lambda2 + ... + \lambdan = 0 \in C
2) I'm not quite sure about what it means that 1=e1 + ... + en
Does it mean that each en is something like <1,0,0...,0>, <0,1,0,...,0>, etc?
3)...
Homework Statement
Let V=Cn and 1 be all ones vector 1 = e1 + ... +en. Let W be the subspace of V spanned by those vectors of the form \lambdae1 + \lambdae2 + ... + \lambdaen such that \lambda1 + ... + \lambdan= 0 \in C. Prove that there is a direct sum decomposition
V=(C*1) \oplus W
as...