On some tensor inequalities based on the t-product
Numerical Analysis
2021-08-10 v1 Numerical Analysis
Functional Analysis
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{\" o}lder inequality, and Minkowski inequality are generalized to tensors. Furthermore, we obtain some t-eigenvalue inequalities.
Cite
@article{arxiv.2108.03892,
title = {On some tensor inequalities based on the t-product},
author = {Zhengbang Cao and Pengpeng Xie},
journal= {arXiv preprint arXiv:2108.03892},
year = {2021}
}