Perron-Frobenius Theorem for Rectangular Tensors and Directed Hypergraphs

Linyuan Lu, Arthur L. B. Yang, James J. Y. Zhao

For any positive integers $r$, $s$, $m$, $n$, an $(r,s)$-order $(n,m)$-dimensional rectangular tensor ${\cal A}=(a_{i_1\cdots i_r}^{j_1\cdots j_s}) \in ({\mathbb R}^n)^r\times ({\m…