Recent content by tazzzdo

Love being in grad school and missing stupid things like that. -__- Preciate the help.

Now I understand. I used 0 1 1 0 and 0 -1 1 0

1 1 0 1 There is no way to make that matrix the sum of 2 normal matrices A and B?

I don't understand how to make a non-normal matrix break down into 2 normal matrices. That's the whole point of my post.

Normal Matrices Examples (URGENT) I need to produce 2 x 2 normal matrices A and B such that A + B is not normal. I have proven that AB is normal if AB = BA using the Householder matrix form. But I can't find a form for A + B failing to be normal. A matrix A with entries a, b, c, d is going...

If each σ is diagonal or anti-diagonal, could I just write each diagonal entry of exp(σ) as e^σij, then add all of the σ's up? Like this case: http://en.wikipedia.org/wiki/Matrix_exponential#Diagonalizable_case

It's problem #5 on this homework set: https://docs.google.com/open?id=0B9c8sp75B5ZRMHAxYXB3MWdhYk0 I can calculate (\pi/4)(n1σ1 + n2σ2 + n3σ3) easily, but I have NO clue how a matrix M = exp[(\pi/4)(n1σ1 + n2σ2 + n3σ3)].

I can't find a transformation n such that n(1) = infinity

Yeah I see what you're saying. Then does that mean I just switch the z's around in (a) for n(z)? But use the same transformation?

Well if I plug those z's in, I get z(-∞)/(z-∞) for m(z). I seem to hit a wall there. Same with n(z). I don't know how to fix those equations into a form that I can use for the composition.

I meant I* lol. Thanks.

Homework Statement H is the upper-half plane model of the hyperbolic space Find all Mobius transformations that send M to N. Homework Equations a) M = {0, 1, ∞}, N = {∞, 0, 1} b) M = {0, 1, ∞}, N = {0, ∞, 2} c) M = {i, -i, 3i}, N = {∞, i + 1, 6} The Attempt at a Solution...

Homework Statement Find all the fixed points to the following Mobius transformation. Homework Equations m(z) = (2z + 5)/(3z - 1) The Attempt at a Solution Aren't all fixed points going to map to themselves? So shouldn't it be solving for m(z) = z and coming up with roots of a quadratic...

You can absolutely prove that x is irrational and therefore xc is irrational and not an integer. 1. Show x is irrational by contradiction. 2. Assume a < xc < b for integers a, b, c, where xc is an integer. 3. Prove that since x is irrational, then xc is also irrational and therefore not an...

Wait I misread this. Something is off...