# Matrix Completion With Deterministic Pattern: A Geometric Perspective

@article{Shapiro2019MatrixCW, title={Matrix Completion With Deterministic Pattern: A Geometric Perspective}, author={Alexander Shapiro and Yao Xie and Rui Zhang}, journal={IEEE Transactions on Signal Processing}, year={2019}, volume={67}, pages={1088-1103} }

We consider the matrix completion problem with a deterministic pattern of observed entries. In this setting, we aim to answer the question: Under what conditions will there be (at least locally) unique solution to the matrix completion problem, i.e., the underlying true matrix is identifiable? We answer the question from a certain point of view and outline a geometric perspective. We give an algebraically verifiable sufficient condition, which we call the well-posedness condition, for the local… Expand

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