A linear gap for the maximal cp-rank
2026-09-27
Research publication
A linear gap for the maximal cp-rank
Preprint
- Original date
- Authors
- Yair Lavi
- Matrix theory
- Completely positive matrices
- Copositive matrices
About this work
Our first non-permanent related result, and it’s a nice one:)
We prove that the maximal cp-rank \(p_n\) satisfies \({p_n\ge n(n-3)/2}\) for odd \({n\ge5}\) and \({p_n\ge n(n-3)/2-1}\) for even \({n\ge6}\). Together with the known upper bound \({p_n\le\binom{n+1}{2}-4}\), this gives \({p_n=n^2/2+O(n)}\).