Eckart-Young Theorem for Tubal Tensors: Conditions and Applications

This paper addresses a fundamental question in tensor analysis: under what conditions does the Eckart-Young theorem, which provides the best low-rank approximation, hold for tubal tensors? This is significant because it extends a crucial result from matrix algebra to the tensor framework, enabling efficient low-rank approximations. The paper's contribution lies in providing a complete characterization of the tubal products that satisfy this property, which has practical implications for applications like video processing and dynamical systems.