  The concept of tensor eigenpairs has received more researches in past
decades. Recent works have paid attentions to a special class of symmetric
tensors termed regular simplex tensors, which is constructed by equiangular
tight frame of n + 1 vectors in n-dimensional space, and the robustness of
eigenpairs was investigated. In the end of the literature, a conjecture was
claimed that the robust eigenvectors of a regular simplex tensor are precisely
the vectors in the frame. One later work theoretically proved that the case of
n = 2 was true. In this paper, we proceed further and complete the proof for
the above conjecture. Some promising directions are discussed in the end for
future works.
