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bio website wolfram.com
location United States
age 37
visits member for 3 years, 9 months
seen 5 hours ago

The gravatar was made with Mathematica, and inspired by this.

The contents of my posts are my own opinion, and do not reflect the opinions of my employer.


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
comment Generating the partners in a multi-dimensional irreducible representation.
Since this has received no traction here, I've asked over at mathoverflow.
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
Jun
8
awarded  Caucus
Apr
18
awarded  Promoter
Apr
16
asked Generating the partners in a multi-dimensional irreducible representation.
Jan
30
comment Pythagorean Theorem Proof Without Words (request for words)
Brilliant. Nice answer.