Recent content by Fellowroot

Okay, now that I'm looking at it, its more than obvious. The red flag that got me was that it mentioned the word sequence and I didn't really get that because I always viewed this as a series not a sequence, as if they were different. But as you have shown me, while you are calculating the...

In my book, applied analysis by john hunter it gives me a strange way of stating an infinite sum that I'm still trying to understand because in my calculus books it was never described this way. It says: We can use the definition of the convergence of a sequence to define the sum of an...

I see that apparently its called phase and its related to angles, but I am missing the other details.

Exactly as stated in the title. What does ph(z) mean?

Oh yeah, apparently you use orthogonal projections.

^ I don't think using cauchy sequences does the job here. my teacher said I want to show closed. i don't see how cauchy shows how these spaces are closed.

Thanks. I think I now have the answer to part 1 because you can use an idea from Parseval which automically shows that en weakly converges to zero. But I'm still not sure about what to do with an and un. I also think the boundedness of an plays a role. For part 2 I know that this is showing...

Homework Statement This is a problem from Haim Brezis's functional analysis book. Homework EquationsThe Attempt at a Solution I'm assuming (e)n is the vectors like (e)1 = (1,0,0), (e)2=(0,1,0) and so on. We know every hilbert space has an orthonormal basis. I also need to know the...

Homework Statement [/B] Let M, N be a subset of a Hilbert space and be two closed linear subspaces. Assume that (u,v)=0, for all u in M and v in N. Prove that M+N is closed. Homework Equations I believe that (u,v)=0 is an inner product space The Attempt at a Solution This is a problem from...

I believe that I've now figured it out. I just used det(a-lamda(I))=0 solve eigen values and then get eigen vectors.

Okay, so this problem was the example problem in my engineering math book. I tried to do the example before getting to the actual problems. Now I tried the same technique on the first problem and I checked out my solution to see if it worked and it only half worked. The problem I'm having is...

Thank you so much! I solved the equation. x(t)=c1t+c2tln(t)+t[ln(t)]^2 the matrix solution seems to be the wronstkian of the functions next to the c1 and c2, however the third term which doesn't have a constant I'm not sure what to do with it or if it has any significant importance.

Homework Statement Find general solution of the given problem in the picHomework Equations All I need to know is where they found the fundamental set of solutions. The Attempt at a Solution All I need to know is where they found the fundamental set of solutions. Please see pic. All I want...

Okay I'm still trying to master this topic. Can someone please explain to me how they got linear dependent on this following problem. u = (e^t,0) v = (0,0) w = (0, e^t) How is this dependent? I cannot for the life of me find something like au + bv = w.

actually i don't think that is so. t-t^2 is not a -2 multiple of -2t+4t^2 the 4 makes it not work like this. Also on number 5 in my homework I have this problem: u = ( 2-t,t,-2) v = (t, -1, 2 ) w = (2+t, t-2, 2 ) it says in the answer is linear dependent, yet how can this be? I do not...