In this lecture note, we discuss a fundamental concept, referred to as the characteristic rank, that suggests a general framework for characterizing the basic properties of various low-dimensional models used in signal processing. We illustrate this framework through two examples-matrix and three-way tensor completion problems-and consider basic properties, including the identifiability of matrices and tensors, given partial observations. We consider cases without observation noise to illustrate the principle.

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关于矩阵和张量完成的特征等级[讲义]

在本讲义中，我们讨论了称为特征等级的基本概念，该概念提出了用于表征信号处理中使用的各种低维模型的基本特性的通用框架。我们通过两个示例（矩阵和三向张量完成问题）说明了该框架，并考虑了部分观察的基本性质，包括矩阵和张量的可识别性。我们考虑没有观察噪声的情况来说明原理。