• DocumentCode
    719265
  • 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
  • fYear
    2015
  • fDate
    25-29 May 2015
  • Firstpage
    197
  • Lastpage
    200
  • 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;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    Sampling Theory and Applications (SampTA), 2015 International Conference on
  • Conference_Location
    Washington, DC
  • Type

    conf

  • DOI
    10.1109/SAMPTA.2015.7148879
  • Filename
    7148879
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=719265