Oops, you are correct, I should have done an outer-product difference there.
Thanks for pointing this out, -- Raul On Thu, Nov 14, 2019 at 8:34 PM Ben Gorte <[email protected]> wrote: > > As to intuition, I started wondering whether your sentences produce > averages of distances between two random points, or between the origin and > a random point (=vector length). Or whether that might be the same (?) > For two points at a time I get: > > avg %: +/ *: -/?2 1000 1000$0 > > 12.8989 > > avg %: +/ *: -/?2 4000 1000$0 > > 25.8177 > > avg %: +/ *: -/?2 10000 1000$0 > > 40.8296 > > (if I'm not mistaken) > > > So it is not the same. In 1D it's 0.33 vs. 0.5 and that ratio seems to hold > in any dimension (which makes sense. Intuitively). > > > Greetings, > > Ben > > > > > > On Fri, 15 Nov 2019 at 03:47, Raul Miller <[email protected]> wrote: > > > For example, here's an illustration of the concept that the average > > distance between random points in a unit hypercube increases with the > > number of dimensions: > > > > (+/%#)+/&.:*:?1000 1000$0 > > 18.2652 > > (+/%#)+/&.:*:?4000 1000$0 > > 36.5102 > > (+/%#)+/&.:*:?10000 1000$0 > > 57.7314 > > > > Thanks, > > > > -- > > Raul > > > > On Thu, Nov 14, 2019 at 11:16 AM Raul Miller <[email protected]> > > wrote: > > > > > > I stumbled across this today: > > > https://github.com/leopd/geometric-intuition accompanied by an > > > assertion that you can find the eigenvectors for a hermitian matrix > > > from its eigenvalues and the eigenvalues of its submatrices. I have > > > not yet worked through the details of that, but it sounds plausible > > > and might be of interest to some of you, here. > > > > > > But the repository itself covers a lot more ground than that. > > > > > > Anyways, the code is python, but a lot of it is fairly straightforward > > > to re-implement, and there's good english descriptions and > > > illustrations, also. So this looks like fun. > > > > > > FYI, > > > -- > > > Raul > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
