Recent content by Mechmathian

Cauchy Shwartz: (x,y)<=||x||*||y||

The thing is that the dot product does not have the modules.. Even if I do maximize it.. I do not see where to go from there..

I think that it is a matrix operator..

Unfortunately I do not understand why |Av|^2=v^(T)*A^T*A*v is true.. Why does it not depend on a_i?? 2. I don't think I know how to proove that the eigenvalues are nonnegative or where to go from there..

(i just need the real case)

By the way, do you want to say that it does nod depend on a_i??

Thanks, but do you know how to proove it?

Homework Statement In R^{3} ||x||= a_{1}*|x_{1}|+ a_{2}*|x_{2}|+ a_{3}*|x_{3}|. where a_{i}>0 What is ||A||(indused norm = sup||Ax|| as ||x||=1). (Suppose we know the coeffisients of the matrix/operator A)?? Homework Equations The Attempt at a Solution

Is there another section that I should ask about the homework problems I have? I don't think anyone of them was yet answered?

Very important! Homework Statement If A is an symmetric operator in separable hilbert space (H) and 1)A>=0 (which means that (Ax, x)>=0 for any x) 2)A(H) is a closed set How do you proove that \sqrt{A}(H) is a closed set Homework Equations The Attempt at a Solution Facts...

Does anyone even know a book, where I could read about those knids of problems!?

The chain is aperiodic 1->3->2->3->1 You can get from any position to any other (it doesn't have to be in one step..)

What I wrote is definitely true.. The other problem on this theme that was given to us is: Is it true that a solution of u_{t}= u_{x} in generalized functions looks locally like f(t+x)?

Yeah)) Sorry!

I'm sorry, maybe I am mistaking on the terms.. A general function is a functional on D- the finite, infinitely differentiable functions