Recent content by Hallingrad

Yeah I know the properties of an inner product. I just don't know what procedure I should use when actually given a matrix with values that multiply two vectors v and w that have unknown values. But how can I use gram-shmidt on an indeterminate number of vectors (i.e. 1 to n)?

Hey guys, In one of the questions for our assignment we have to decide whether <v,w> = v^{}TAw (with a conjugate bar over w) defines an inner product on C3. We are given three 3x3 marices to test this. What is the procedure for doing this? Do we just give w and v values such as a1, a2, a3...

Making it not null didn't help. It seems that any nodes made in the while loop get turned into what the last node was before the while loop exits, but if I manually add another node after that, it doesn't affect the previous nodes. Frankly I'm at a loss after hours of staring at the code.

Making it null was just one of the various solutions I tried to rectify the problem. It didn't change the output when traveling through the list, but you're right, I should probably remove it. As for the firstNode, where would I place it? The way I designed it, I'm adding new nodes to the...

Hey guys, I'm trying to implement a linked list in C, with each node carrying fields from a text file. The problem is that whatever was the last line read from the text file gets placed into every single node. Even more strange is that when I add an additional node outside of the while loop it...

Two questions. First, I'm given a 3x3 matrix with the last row all zeroes. I'm asked to diagonalizable it, but the determinant is 0, so there are no eigenvalues. Am I reasoning correctly here? It seems an odd question to ask. Second, I'm asked to prove that if A n x n matrix in C space, then...

After another week of classes, he still hasn't addressed invariant transformations. I understand that the image is to the column space as the kernel is to the nullspace for a transformations. That is, the image is what is the output of a given transformation. Yet I still don't see how T(im(T)) =...

I have a loose grasp on why that may be, but what's the formal proof?

With that in mind though, how do you show that T(im(T) = im(T)? That is what we're trying to show, right? And what about the intersection of W1 and W2?

Well we haven't yet covered what an invariant transformation is, but the assignment is due before the next lecture :/. Any advice on where to start?

Hey guys, I was wondering how you would go about proving that the image of a transformation T, im(T), is invariant? And following that, how would you prove T(W1 \bigcap W2) is invariant if T(W1) and T(W2) are both invariant. On an unrelated note, another questions asks to show that TX =...

Here are my answers to the proofs. Could you let me know what you think? For a) I wrote "A is a matrix that maps a vector from Fn to Fm. Each v lies in Fn, and is then transformed by A to lie in W, which is in Fm. U is a subspace of Fn, and consists of all such vectors that are in Fn and that...

So for the first part, because the v's lie in Fn and W is in Fm, the v's don't actually lie in W, correct? Instead the transformation under A brings them into W, so we'd have to show that Av1 and Av2 form a subspace?

Yeah, I think I can write it as such. The only thing I'm unclear of as is to why v1 and v2 lie in W when the v's are in Fn while W is in Fm?

Wait, isn't W in Fm, while v1 and v2 are in Fn? Aren't v1 and v2 only in W (and hence Fm) upon being mapped by A?