3 problems

For a tensor dimension $n_1\times n_2\times\dots\times n_d$, let $\phi(\mathbb{R}^{n_1\times n_2\times\dots\times n_d}_+)$ be the infimum of the spectral-to-Frobenius norm ratio ov…

Let $2\le n=\prod_{k=1}^{s_n}p_k$ be the prime factorization, with $2\le p_1\le p_2\le\dots\le p_{s_n}$. Consider a tensor…

Let $\boldsymbol{\beta}$ denote the lower bound in equation (main) for the ratio of the spectral norm to the Frobenius norm. An unfolded permutation tensor is a tensor obtained by…