Timeline for An optimal subspace projection problem

8 events

when toggle format	what		by	license	comment
Apr 24, 2020 at 8:44	history	edited	Paul	CC BY-SA 4.0	provide additional information
Oct 26, 2017 at 5:08	comment	added	Neal Young		Isn't that the same in the following sense (keeping in mind that we restrict to $v$ with $\\|v\\|_2=1$)? $J$ minimizes the diameter of the projection of $S_k$ onto $\mathbb{R}^n_J$ if and only if $I = [n]\setminus J$ maximizes the length of the smallest principal axis of the projection of $S_k$ onto $\mathbb{R}^n_I$.
Oct 26, 2017 at 4:07	comment	added	Paul		@NealYoung Yes, but what I need here is actually to make the smallest principal axes of the projected ellipsoid to be maximum.
Oct 26, 2017 at 3:46	comment	added	Neal Young		Is this equivalent to the following problem? Given a $k$-dimensional sphere $S_k$ in $\mathbb{R}^n$, find an index set $I$ of size $m$ so that the projection of $S_k$ onto $\mathbb{R}^n_I$ has minimum diameter, where $\mathbb{R}^n_I$ is the linear subspace spanned by the $m$ axes with coordinate indices in $I$.
Oct 23, 2017 at 15:12	history	tweeted			twitter.com/StackCSTheory/status/922480937014841345
Oct 22, 2017 at 19:53	comment	added	Paul		@usul yes, it is.
Oct 22, 2017 at 15:45	comment	added	usul		When you say "projection to the coordinates indexed by $I$", you mean coordinates of the standard basis of $\mathbb{R}^n$?
Oct 22, 2017 at 8:24	history	asked	Paul	CC BY-SA 3.0