In this paper, we consider the contractive real symmetric matrix completion problems motivated in part by studies on sparse (or dense) matrices for weighted sparse recovery problems and rating matrices with rating density in recommender systems. We completely characterize symmetric patterns P with the property (C) that every partially contractive real symmetric matrix with pattern P has a contractive real symmetric completion using graphs.

中文翻译：

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与图相关的收缩对称矩阵完成问题

在本文中，我们考虑了收缩实对称矩阵完成问题，部分原因是对加权稀疏恢复问题的稀疏（或密集）矩阵和推荐系统中具有评级密度的评级矩阵的研究。我们用属性 (C) 完全表征对称模式P ，即每个具有模式P的部分收缩实对称矩阵都具有使用图的收缩实对称完成。