rcollyer
Reputation
929
Top tag
Next privilege 1,000 Rep.
Create tags
 Mar12 answered How to explain brackets to young students Dec15 awarded Caucus Oct10 comment Prove that the sum of three consecutive squares, minus two is a multiple of 3 That is a clever shift compared to John's answer. Oct3 awarded Yearling Dec3 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. Dec3 comment Independent components of trace? @Hunter I've added an additional explanation. Let me know if it helps. Dec3 revised Independent components of trace? added 666 characters in body Dec3 answered Independent components of trace? Oct3 awarded Yearling Sep12 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. Sep12 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 $A$. Aug5 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. Jun1 revised Generating the partners in a multi-dimensional irreducible representation. added 1 characters in body Jun1 comment Generating the partners in a multi-dimensional irreducible representation. Since this has received no traction here, I've asked over at mathoverflow. Jun1 awarded Informed May6 awarded Caucus Jan1 awarded Excavator Jan1 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 Oct3 awarded Yearling Jun8 awarded Constituent