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arXiv · 1502.04656

A small frame and a certificate of its injectivity

Cynthia Vinzant
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Abstract

We present a complex frame of eleven vectors in 4-space and prove that it defines injective measurements. That is, any rank-one $4\times 4$ 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.

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Cynthia Vinzant. 2015-02-16. A small frame and a certificate of its injectivity. https://arxiv.org/abs/1502.04656

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