Research Paper#Tensor Analysis, Low-Rank Approximation, Eckart-Young Theorem🔬 ResearchAnalyzed: Jan 3, 2026 17:13
Eckart-Young Theorem for Tubal Tensors: Conditions and Applications
Published:Dec 30, 2025 18:38
•1 min read
•ArXiv
Analysis
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.
Key Takeaways
- •Identifies the conditions under which the Eckart-Young theorem applies to tubal tensors.
- •Provides a complete characterization of the relevant tubal products.
- •Demonstrates practical applications in video data and dynamical systems.
Reference
“The paper provides a complete characterization of the family of tubal products that yield an Eckart-Young type result.”