Recent content by blanik

The question is "starting from v(t) = Vm cos(wt+theta), show analytically that the RMS value of v(t) is v(t)=Vm/sqrt(2) for any w or theta." I'm not really sure how to begin this. Do I start by taking the integral?

What if I were to find the eigenvectors of the product matrix of (H1)(H2) since (H1)(H2) = (H2)(H1)?

Well, the question specifically states the following: "Find the eigenvectors common to both. (Note: Both matrices have degenerate eigenvalues. You will need to compare the eigenvectors of the two matrices and determine a set of three orthogonal eigenvectors common to both matrices.)" So...

Thanks, that's helpful. Here is where I'm stuck... I checked my math and I am not finding any errors that are standing out. The eigenvectors I came up with are: H1: |v1> = |v2> = ( 1 1 -1/3) and |v3> = (1/3 0 1 ) H2: |u1> = |u2> = (1/3 1 1 ) and |u3> = ( 1 0 -1/3) These are...

I am having a hard with parts of this problem: Suppose V is a 3-dimensional complex inner-product space. Let B1 = {|v1>,|v2>,|v3>} be an orthonormal basis for V. Let H1 and H2 be self-adjoint operators represented in the basis B1 by the Hermitian matrices. I won't list them, but they...

|a>=alpha|b> means the vector A equals alpha times the vector B where alpha is a real positive scalar. Does that help? I understand that I am "supposed" to start with one way and go the other, but what does that mean? Do I substitute a=alpha b for a and solve for ||alpha b + b|| = ||alpha b||...

I have proven the triangle inequality starting with ||a+b||^2 and using the Schwartz Inequality. However, the next part of the problem says: "Show that the Triangle Inequality is an equality if and only if |a>=alpha|b> where alpha is a real positive scalar." It must be proved in both...

I'm not sure where to start with these proofs. Any suggestions getting started would be appreciated. 1. Show that is A,B are linear operators on a complex vector space V, then their product (or composite) C := AB is also a linear operator on V. 2. Prove the following commutator...

He did give us that formula, but how do I use that without actual numbers for A & B? Should I make I = A and sigma x = B and then sigma y = C and sigma z = D? Then I have <A|B> = 1/2Trace(AtB) (where t = Hermitian conjugate) and <C|D> = 1/2Trace(CtD)? So, for the real numbers, i.e. the...

I thought that the hint might be wrong... thanks for clarifying. I caught my math error too for the zero value in the inverse matrix. Thanks so much for your help!

Well, the inner product is defined as |A||B|cos (angle). I don't have numbers for A & B. He says use the inner product for "general" 2x2 matrices A & B. Also, I must not understand orthonormal very well. If the two vectors are orthonormal, then they are perpendicular. The dot product which I...

Thanks! That helped a lot. I am much closer, but I am still not coming up the same numbers for his |e1>. Here is what I did: If a1,a2 &a3 = matrix A, then A = 1 1 0 0 2 -3 -1 1 2 The determinant of A = 10 The inverse of A is: A-1 = (1/10) 7 -2 -3...

My other problem is: Consider now the space of 2x2 complex matrices. Show that the Pauli Matrices |I>= 1 0 0 1 |sigma x>= 0 1 1 0 |sigma y>= 0 -i i 0 |sigma z>= 1 0 0 -1 form an orthonormal basis for this space...

I have two homework problems that I am at a loss on where to start. I am going to see the TA tomorrow, but I would like to start on the problems tonight. The question is (the row vectors I show are actually written as column vectors on the homework): Consider the real vector space R>3...