The probability that a subspace contains a positive vector

TL;DR

This paper calculates the likelihood that a randomly chosen subspace in Euclidean space includes a positive vector, providing insights into geometric probability and subspace properties.

Contribution

It introduces a method to determine the probability that a random subspace contains a positive vector, a novel geometric probability result.

Findings

Derived explicit probability formulas for subspaces containing positive vectors

Extended understanding of geometric properties of random subspaces

Potential applications in convex geometry and high-dimensional probability

Abstract

We determine the probability that a random k-dimensional subspace of Euclidean n-space contains a positive vector.