1
vote
2answers
53 views

Choosing sets of vectors on a complex sphere

Consider a complex $t$ dimensional unit sphere. Can we have $t$ sets of $2^t$ vectors $v_{ij}\in \Bbb C^t$ on the sphere where $i=1$ to $t$ and $j=1$ to $2^t$ on this with inner products satisfying ...
1
vote
1answer
24 views

Choosing vectors on a complex sphere

Consider a complex $t$ dimensional unit sphere. Say we pick $n$ points on this with inner products in the set $\{a_1,a_2,\dots,a_r\}$ (we have $n$ inner products with value $1$). Note the set ...
5
votes
1answer
195 views

Characterisation of linearly separable points of a hypercube

Essentially, linearly separable points are just those corners that can be cut off with just one slice as marked out by a hyperplane. E.g. for a cube, the following 4 points (red) are not linearly ...
4
votes
0answers
77 views

Linear Independence Game

Suppose you have a set $X$ of vectors in $\mathbb{F}_2^n$, with $|X| \ge n+1$, and consider the following game. On their turn, each player (2 player game) chooses from $X$ one vector and sets it aside ...
2
votes
0answers
90 views

Sorting combinations of linearly independent vectors

Given a set of $m$ vectors in $\mathbb{R}^n$ ($m > n$), sort all combinations of $n$ linearly independent vectors according to the determinant of the matrix whose columns are the $n$ vectors. ...
5
votes
0answers
166 views

Points and lines covering them

Let $n$ be a positive integer. A subset $S$ of points in plane satisfies the following conditions: a) We can't find $n$ lines in plane, such that every element of $S$ belongs to at least one of these ...