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A small frame and a certificate of its injectivity
February 16, 2015 · Declared Dead · 🏛 International Conference on Sampling Theory and Applications
"No code URL or promise found in abstract"
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Authors
Cynthia Vinzant
arXiv ID
1502.04656
Category
math.FA
Cross-listed
cs.IT,
math.AG
Citations
72
Venue
International Conference on Sampling Theory and Applications
Last Checked
2 months ago
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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