I am trying to prove that
I have managed to prove one inclusion
The fact that any function in these spaces is a linear transformation was really helpful however if doesn't seem to really help me on the reverse inclusion.
since is a linear transformation:
I dont think this helps me. I can't necessarily say and
What should I do from here? Is this the right path and I'm just not catching something?
Sorry, I have another question having to do with this particular equality.
I've read you can use this to prove that
by asserting that they have the same dimension.
I have been playing around with this for the past hour or so. And haven't really gotten anywhere.
but I have found no equalities that I could apply to.
from the first 3 posts, we know that they are equal (the annihilator of the sum, and the intersection of the annihilators). so they have to have the same dimension.
(assuming, of course, that their dimension is finite).
i may be mistaken, but i am wondering if what the thread starter is asking is, can we show equality from a dimensional argument?
i think we can, but we're going to have to invoke a basis, at some point.
(was your "non-obvious" assertion ?)
ok, i got it. yes, the similarity DID confuse me. and in the case we're talking about:
Ann(W1+W2) = Ann(W1)∩Ann(W2) DOES imply Ann(W1∩W2) = Ann(W1)+Ann(W2)
for a moment, there, we were talking about our conversation, and i got "meta-lost".