rcollyer
Reputation
959
Top tag
Next privilege 1,000 Rep.
Create new tags
 Apr 6 comment Prove over matrix norm and eigenvalues This belongs on Mathematics. This site is for Mathematica questions. Aug 19 comment Generating the partners in a multi-dimensional irreducible representation. Interesting. It did not occur to me to try that. Give me a couple of days to look at it, as it has been a while since I did anything with this. Mar 12 answered How to explain brackets to young students Dec 15 awarded Caucus Oct 3 awarded Yearling Dec 3 comment Independent components of trace? I don't think there is an explicit explanation, other than it is a number, and it corresponds to the 1D representation of $SO(3)$. One of the nice consequences of it being a representation, is representations don't mix with the others under the group action. This simplifies some analyses, and can allow you to block diagonalize the matrix. Now, it is not independent of the diagonal elements, but the use of the trace is effectively a change of variables. Dec 3 comment Independent components of trace? @Hunter I've added an additional explanation. Let me know if it helps. Dec 3 revised Independent components of trace? added 666 characters in body Dec 3 answered Independent components of trace? Oct 3 awarded Yearling Sep 12 comment Pure maths vs applied @jkn as a counter-point to that, my experience with math students though was interesting. In all of the advanced calc courses, I was always way ahead of what they were doing/understood because of the physics courses, and simultaneously, the physics courses made more sense because of the math. Being ahead of the math students did not apply to real analysis as nobody was ahead in that class. Overall, though, they complemented each other very well. Sep 12 comment Eigenvalues and the Characteristic Equation Additionally, if some $\lambda_i = 0$, then $A$ is not invertible, and the eigenspace corresponding to $\lambda_i$ is the null space of $A$. Aug 5 comment Prove that matrix $A = U^{-1}HU$ is Hermitian I believe you meant to post this on Mathematics. This site is for the software program Mathematica, not mathematics. Jun 1 revised Generating the partners in a multi-dimensional irreducible representation. added 1 characters in body Jun 1 awarded Informed May 6 awarded Caucus Jan 1 awarded Excavator Jan 1 revised Can we construct a Hilbert space where the operator $A_u v := -\frac{1}{2} v'' + (vF + v\int_\mathbb{R} Su + u\int_\mathbb{R} Sv )'$ is symmetric? changed apostrophe to ^\prime; spelling Oct 3 awarded Yearling Jun 8 awarded Constituent