We distinguish two types of matrix completion: matrix completion when a subset of entries is observed, and matrix completion when a linear functional of the entire matrix is observed. SVT, and the papers below, deal with the first type; for an introduction to the latter type (which is in some sense an extension of compressed sensing), Guaranteed minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization, by Recht, Fazel and Parrilo, is a good place to start.



  • Above:
    Pictorial representation of the nuclear ball, i.e. 2 x 2 matrices with nuclear norm at most 1.

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