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Jan
2
comment Infinite series with a rising factorial?
You're right, my mistake.
Sep
12
comment Scale invariance and the Mellin transform?
That must be the case being referred to when talking about the "scale-invariant" Mellin transform.
Sep
12
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.
Sep
3
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.
Aug
13
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.
Jul
17
comment Algorithm for finding set of all parents recursively
Agreed. That's why I post things on math.SE :)
Jul
17
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.
Jul
17
comment Algorithm for finding set of all parents recursively
Of course, one could brute force it. But there is probably something more elegant.
Jul
17
comment Algorithm for finding set of all parents recursively
Yes, that will find a set for one vertex. What about all?
Jul
17
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.
Mar
21
comment Singular values of a diagonal matrix concatenated with a vector?
Interesting...how would I use that to get the singluar values?
Mar
21
comment Singular values of a diagonal matrix concatenated with a vector?
Yes, copper.hat and Git Gud are correct.
Mar
12
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?
Mar
12
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 $(I-xx^T)Q(I-xx^T) + xx^TQ(I-xx^T) + (I-xx^T)Qxx^T + xx^TQxx^t = h + xg^T + gx^T + f(x).$
Mar
8
comment Prove that there are no convex functions on compact manifolds
What about continuous but non-smooth functions?
Feb
22
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.
Feb
22
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.
Feb
22
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?
Feb
22
comment Solve a quadratic matrix equation?
It's an invertible matrix, so that's the square of the inverse
Feb
20
comment Fit a quadratic form given covariant derivatives on the sphere?
let us continue this discussion in chat