bio | website | math.ucsd.edu/~jpascoe |
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location | University of California, San Diego | |
age | 24 | |
visits | member for | 1 year, 9 months |
seen | 7 hours ago | |
stats | profile views | 197 |
I am a graduate student at University of California, San Diego under the advice of Jim Agler.
Dec 4 |
asked | Calculating the dimension of the algebra generated by some given matrices |
Sep 17 |
comment |
Does this simple inequality have a name?
I guess this is equivalent to the inequality $x^2 \leq x(m+M) - Mm,$ since it must be true term by term ($n=1$ case seems to imply the claim in general). So that inequality might have a name if such a thing exists. The fact that $M \geq x$ then immediately implies the claim, so it might not, because it could be seen as being too easy, since it doesn't seem like there's any trick. |
Sep 7 |
accepted | Moments of the trace of orthogonal matrices |
Sep 6 |
awarded | Autobiographer |
Sep 5 |
comment |
Moments of the trace of orthogonal matrices
This is an amazing amount of data. I wonder if it's in any of the triangles in the OEIS (Like Pascal's triangle or Stirling numbers.) |
Sep 5 |
awarded | Nice Question |
Sep 5 |
awarded | Curious |
Sep 4 |
revised |
Moments of the trace of orthogonal matrices
edited body |
Sep 4 |
comment |
Moments of the trace of orthogonal matrices
I don't really know what you mean by $A'$ above, nor do I know enough about the values of zonal polynomials. However since I think I am calculating $E_X[\text{tr}(X)^k]$ in your language, is it the case that we will have some cancellation in this formula (the $\lambda$ might cancel the zonal polynomial factors out, but I don't know what you mean by scaling)? (Also in the denominator do you mean $(2k)!$ or $2(k!)$? I guess there's also a similar question about the numerator.) |
Sep 4 |
comment |
Moments of the trace of orthogonal matrices
Thanks. This is the formula I spotted. However, I want a formula for that holds for large $k,$ (in some sense the $n$ I am choosing is small and fixed) for example if $n=3.$ The above formula doesn't give me enough information. |
Sep 4 |
asked | Moments of the trace of orthogonal matrices |
Aug 19 |
comment |
Is there an algebraic number that cannot be expressed using only elementary functions?
In your post on stackexchange you allowed $i,$ and other elemenary complex analysis: do you still want to do this? It seems if you include integration, it would be possible to express any algebraic number this way. Anyway for an algebraic number $a$ with minimum polynomial $p,$ $a = \int_{\gamma} \frac{zp'(z)}{p(z)} dz,$ where $\gamma$ is a circle with rational radius and center, containing $a$ and no other roots of $p.$ |
Aug 7 |
comment |
Invertibility of random Vandermonde matrix
Yeah, you definitely need to use non-atomicity. I think you need something a bit stronger, since if the points lie in certain varieties, you may run into trouble. |
Aug 7 |
answered | Invertibility of random Vandermonde matrix |
Aug 4 |
comment |
What summations of elementary trig functions are known to have (elementary) closed forms?
If you mean $\Sigma^{\infty}_{k=0} \tan{k},$ I think that sum does not converge. Can you be more explicit about what sums you're talking about? |
Aug 3 |
comment |
largest eigenvalue of a symmetric matrix
I mean $I$ to be the N by N identity matrix. |
Aug 3 |
comment |
largest eigenvalue of a symmetric matrix
Then it would seem that taking $\Phi = -I$ and $P = I,$ where I, would imply that the phenomenon is indeed a coincidence. Although, with some extra special structure, the phenomenon may hold. |
Aug 3 |
comment |
largest eigenvalue of a symmetric matrix
What is $\Phi?$ |
Jul 31 |
awarded | Enlightened |
Jul 31 |
awarded | Nice Answer |