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New bounds for eigenvalues of strictly diagonally dominant tensors

* Corresponding author: Wei Wu

This work was supported by NSF grant of China (Grant No. 11371276).

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  • 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.

    Mathematics Subject Classification: Primary: 15A18, 15A69, 65F15.

    Citation:

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