Title :
A small frame and a certificate of its injectivity
Author :
Vinzant, Cynthia
Author_Institution :
Dept. of Math., North Carolina State Univ., Raleigh, NC, USA
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 × 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.
Keywords :
Hermitian matrices; signal processing; Hermitian matrix; algebraic certificate; algebraic computation; finite-dimensional frame; injective measurement; signal processing; vector collection; Algebra; Current measurement; Electronic mail; Geometry; Imaging; Polynomials;
Conference_Titel :
Sampling Theory and Applications (SampTA), 2015 International Conference on
Conference_Location :
Washington, DC
DOI :
10.1109/SAMPTA.2015.7148879
