Recent content by wakko101

I'm currently working on a lab that is exploring the Raman effect. One of the suggested exercises was to record the raman spectrum (from a mercury lamp through CCl4) around the rayleigh peaks at 435.8 nm and 404.7 nm. For the former, my results were fairly consistent with what I expected in that...

Homework Statement Consider 2 circles. For every couple of circles consider their two common external tangent lines and take their point of intersection. Prove that these 3 points of intersection belong to one line. Homework Equations Menelaus' theorem, possible Ceva's theorem as well...

If it is onto, we can use the first isomorphism th. to get the order of the kernel which would be 12. I know that a kernel must be a normal subgroup of A(4) and I've figured out (i.e. read somewhere) that the only normal subgroup of A(4) has order 3. So, using that, I can see how we might prove...

Homework Statement Show that there is no homomorphism from A(4) onto a group of order 2, 4 or 6, but that there is one onto a group of order 3. Homework Equations I have a feeling that I'm to use the First Isomorphism theorem The Attempt at a Solution I've been puzzling over this for...

The question: Let n > 1 be a fixed integer and let G be a group. If the set H = {x in G : |x| = n} together with the identity forms a subgroup of G, what can be said about n? I know that n must be prime, but I can't figure out why that would be. The elements of h only have order 1 or n...

I'm a bit confused about something. Does the parity of a permutation (i.e. if it is even or odd) tell you if the order of the permutation is even or odd, or are they unrelated? Any insight would be appreciated. Cheers, W. =)

I believe so... b^(2n)ba = ab^(2n)b b^2n(ba) = b^2n(ab) since abb = bba ba = ab If that's it, then cheers! =)

I was going over a proof in which the following is given: if abb=bba and b is of odd order, then ab=ba (i.e. if b^2 centralizes a then so does b) I'm not sure why this is so. Any clarification would be appreciated. Cheers, W. =)

Homework Statement Calculate the difference between the binding energy of a nucleus of carbon 12 and the sum of the binding energies of three alpha particles. Assuming the carbon 12 is composed of three alpha particles in a triangular structure, with three effective "alpha bonds" joining them...

One place to start would be to use Lagrange's theorem...Since Z6 has order 6, you know that any subgroup can only have order 1, 2 or 3 (and 6, but then this is Z6 itself). You also know that any subgroup must have the identity in it so that narrows your search down as well. Since (I believe) Z6...

I'm not entirely sure this is correct, but I've come up with the following: If (X^T)AX > 0 then we have (Y^T)DY > 0 (for X = PY and D = (P^T)AP). This implies that the entries on the diagonal matrix D (the eigenvalues) are all positive. So, write D = (Q^T)Q where Q is the diagonal matrix of the...

I think you should only be getting one triangle. Try checking your picture against one generated by a graphing tool. Cheers, W. =)

Homework Statement Given a real symmetric matrix A, prove that: a) A is positive definite if and only if A = (B^T)B for some real invertible matrix B b) A is positive semidefinite if and only if there exists a (possibly singular) real matrix Q such that A = (Q^T)Q Homework Equations...

If A and B are groups, then A x B is a group...does the same hold for subgroups? i.e. if A' is a subgroup of A and B' for B, then is A' x B' a subgroup of A x B? Cheers, W. =)

Homework Statement Let G = GL(2, R). Define P : G to G by P(A) = The inverse of the transpose of A (ie. ((A)tr)^-1). P is an automorphism of G, prove that P is not an inner automorphism of G. That is, prove that there does not exist a fixed matrix B in G such that P(A) = BAB^-1 for all A in G...