  In this lecture note, we discuss a fundamental concept, referred to as the
{\it characteristic rank}, which suggests a general framework for
characterizing the basic properties of various low-dimensional models used in
signal processing. Below, we illustrate this framework using two examples:
matrix and three-way tensor completion problems, and consider basic properties
include identifiability of a matrix or tensor, given partial observations. In
this note, we consider cases without observation noise to illustrate the
principle.
