J. E. Pascoe
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 Dec 25 awarded Popular Question Apr 27 accepted Approximating the norm of an operator-valued linear function with operator inputs via a matrix-valued linear function Apr 27 comment Approximating the norm of an operator-valued linear function with operator inputs via a matrix-valued linear function In the exact case, how do you get the projections? Apr 27 asked Approximating the norm of an operator-valued linear function with operator inputs via a matrix-valued linear function Mar 16 comment A conjecture regarding the integral of the square of an entire function What about the function $f(t) = (\sin^2(t) + e^{-t})^t?$ Feb 6 awarded Disciplined 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