# Extreme ratio between spectral and Frobenius norms of nonnegative tensors

@article{Cao2022ExtremeRB, title={Extreme ratio between spectral and Frobenius norms of nonnegative tensors}, author={Sheng Cao and Simai He and Zhening Li and Zhen Wang}, journal={ArXiv}, year={2022}, volume={abs/2206.07879} }

One of the fundamental problems in multilinear algebra, the minimum ratio between the spectral and Frobenius norms of tensors, has received considerable attention in recent years. While most values are unknown for real and complex tensors, the asymptotic order of magnitude and tight lower bounds have been established. However, little is known about nonnegative tensors. In this paper, we present an almost complete picture of the ratio for nonnegative tensors. In particular, we provide a tight…

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