On a multi-dimensional generalization of the notions of orthostochastic and unistochastic matrices

We introduce the notions of dd-orthostochastic, dd-unistochastic, and dd-qustochastic matrices. These are the particular cases of FdFd-bistochastic matrices for F=R,C,HF=R,C,H. The concept is motivated by mathematical physics. When d=1d=1, we recover the orthostochastic, unistochastic, and qustochastic matrices respectively. Here we expose the basic properties of FdFd-bistochastic matrices.