NEW BOUNDS FOR EIGENVALUES OF STRICTLY DIAGONALLY DOMINANT TENSORS

摘要

In this paper, we prove that the minimum eigenvalue of a strictly diagonally dominant Z-tensor with positive diagonal entries lies between the smallest and the largest row sums. The novelty comes from the upper bound. Moreover, we show that a similar upper bound does not hold for the minimum eigenvalue of a strictly diagonally dominant tensor with positive diagonal entries but with arbitrary off-diagonal entries. Furthermore, other new bounds for the minimum eigenvalue of nonsingular M-tensors are obtained.