David Pfau
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 Jan2 comment Infinite series with a rising factorial? You're right, my mistake. Sep12 comment Scale invariance and the Mellin transform? That must be the case being referred to when talking about the "scale-invariant" Mellin transform. Sep12 comment Scale invariance and the Mellin transform? But that's a trivial case. Any transform of a scale-invariant function will be scale-invariant, by definition. Sep3 comment How are definitions of chaos related? No, but I did come across the Pesin article they cite. It's well over my head though. Hopefully there is a good resource that covers the results from that article in a more accessible presentation. Aug13 comment Multilinear or Tensor Regression? No - there is the difference between a linear map (a matrix) and a multilinear map (a higher-rank tensor), which is a kind of nonlinear map. Jul17 comment Algorithm for finding set of all parents recursively Agreed. That's why I post things on math.SE :) Jul17 comment Algorithm for finding set of all parents recursively Ah, I realize I was too general in what I was describing. I also want $A$ to have the property that there is no other set $B$ that contains all the parents of elements such that $A \subset B$. So in that case, you would first have to find the minimal elements of the graph, then apply this algorithm at those elements. Jul17 comment Algorithm for finding set of all parents recursively Of course, one could brute force it. But there is probably something more elegant. Jul17 comment Algorithm for finding set of all parents recursively Yes, that will find a set for one vertex. What about all? Jul17 comment Algorithm for finding set of all parents recursively I suspect there is a graph theory term for what I'm trying to compute, but I am not aware of it. It's not the same as strongly connected components, although any strongly connected component should be a subset of the full set to be unioned. Mar21 comment Singular values of a diagonal matrix concatenated with a vector? Interesting...how would I use that to get the singluar values? Mar21 comment Singular values of a diagonal matrix concatenated with a vector? Yes, copper.hat and Git Gud are correct. Mar12 comment Fit a quadratic form given covariant derivatives OK, so say we can solve for Q up to some constant factor on the diagonal. That means we could still solve for the eigenvectors of Q, right? Mar12 comment Fit a quadratic form given covariant derivatives Right, it actually turns out to be almost trivial. Let $g = (I-xx^T)Qx$, let $h = (I-xx^T)Q(I-xx^T)-(x^TQx)(I-xx^T)$. You can expand $Q$ as $(I-xx^T)Q(I-xx^T) + xx^TQ(I-xx^T) + (I-xx^T)Qxx^T + xx^TQxx^t = h + xg^T + gx^T + f(x).$ Mar8 comment Prove that there are no convex functions on compact manifolds What about continuous but non-smooth functions? Feb22 comment Solve a quadratic matrix equation? I suppose there is slightly more structure. $b$ is $-\mathrm{Tr}M/n = -\sum_i \lambda_i/n$ where $n$ is the dimension of the matrix, and $a = \frac{n-1}{n}$. So that might simplify the numerator considerably. Feb22 comment Solve a quadratic matrix equation? This problem came from trying to solve this problem: math.stackexchange.com/questions/307623/…. In my partial solution I show how I got to an equation of this form. Feb22 comment Solve a quadratic matrix equation? No, there isn't any particular structure to the spectrum of M. Short of an analytic solution, are there algorithmic methods suited to finding roots of rational functions like this one? Feb22 comment Solve a quadratic matrix equation? It's an invertible matrix, so that's the square of the inverse Feb20 comment Fit a quadratic form given covariant derivatives on the sphere?