A small frame and a certificate of its injectivity
Functional Analysis
2015-02-17 v1 Information Theory
Algebraic Geometry
math.IT
Abstract
We present a complex frame of eleven vectors in 4-space and prove that it defines injective measurements. That is, any rank-one Hermitian matrix is uniquely determined by its values as a Hermitian form on this collection of eleven vectors. This disproves a recent conjecture of Bandeira, Cahill, Mixon, and Nelson. We use algebraic computations and certificates in order to prove injectivity.
Keywords
Cite
@article{arxiv.1502.04656,
title = {A small frame and a certificate of its injectivity},
author = {Cynthia Vinzant},
journal= {arXiv preprint arXiv:1502.04656},
year = {2015}
}
Comments
4 pages, 3 figures