Abstract
The H-matrices are an important class in the matrix theory, and have many applications. Recently, this concept has been extended to higher order ℋ-tensors. In this paper, we establish important properties of diagonally dominant tensors and ℋ-tensors. Distributions of eigenvalues of nonsingular symmetric ℋ-tensors are given. An ℋ+-tensor is semi-positive, which enlarges the area of semi-positive tensor from M-tensor to ℋ+-tensor. The spectral radius of Jacobi tensor of a nonsingular (resp. singular) ℋ-tensor is less than (resp. equal to) one. In particular, we show that a quasi-diagonally dominant tensor is a nonsingular ℋ-tensor if and only if all of its principal sub-tensors are nonsingular ℋ-tensors. An irreducible tensor A is an ℋ-tensor if and only if it is quasi-diagonally dominant.
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Wang, X., Wei, Y. ℋ-tensors and nonsingular ℋ-tensors. Front. Math. China 11, 557–575 (2016). https://doi.org/10.1007/s11464-015-0495-6
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DOI: https://doi.org/10.1007/s11464-015-0495-6