A note on the Steinitz Lemma

TL;DR

This paper explores the Steinitz problem, linking the ordering of vector families in various norms to a variant involving nearly unit vectors, expanding understanding of vector arrangements.

Contribution

It establishes a new connection between the classical Steinitz problem and a variant involving nearly unit vectors in arbitrary norms.

Findings

Connected Steinitz problem with nearly unit vector variants

Extended understanding of vector ordering in different norms

Provided new insights into vector family arrangements

Abstract

We establish the connection between the Steinitz problem for ordering vector families in arbitrary norms and its variant for not necessarily zero-sum families consisting of `nearly unit' vectors.