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We introduce the notions of $d$-orthostochastic, $d$-unistochastic, and$d$-qustochastic matrices. These are the particular cases of $F^d$-bistochasticmatrices where $F$ is real or complex numbers or quaternions. The concept ismotivated by mathematical physics. When $d=1$, we recover the orthostochastic,unistochastic, and qustochastic matrices respectively. This work exposes thebasic properties of $F^d$-bistochastic matrices.

On a multi-dimesional generalization of the notion of orthostochastic and unistochastic matrices