A Simple Proof for Efficient Federated Low Rank Matrix Recovery from column-wise Linear Projections

This note provides a significantly simpler and shorter proof of our sample complexity guarantee for solving the low rank column-wise compressive sensing (LRCS) problem using the Alternating Gradient Descent (GD) and Minimization (AltGDmin) algorithm. AltGDmin was developed and analyzed for solving LRCS in our recent work. We also provide an improved guarantee.