On some tensor inequalities based on the t-product

2021/08/09 by Zhengbang Cao, Pengpeng Xie, Cao, Zhengbang +1
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2108.03892

openalex publication_date 2021/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we investigate the tensor inequalities in the tensor t-product formalism. The inequalities involving tensor power are proved to hold similarly as standard matrix scenarios. We then focus on the tensor norm inequalities. The well-known arithmetic-geometric mean inequality, H" older inequality, and Minkowski inequality are generalized to tensors. Furthermore, we obtain some t-eigenvalue inequalities.

Citations

• Some Mathematical Notes on Three-Mode Factor Analysis
• Analysis of Individual Differences in Multidimensional Scaling Via an N-way Generalization of “Eckart-Young” Decomposition
• Factorization strategies for third-order tensors
• Tensor Robust Principal Component Analysis with a New Tensor Nuclear Norm

Related

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• A note on perturbation analysis for T-product based tensor singular values
• T product Tensors Part II: Tail Bounds for Sums of Random T product Tensors
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