Some New Properties Of M-tensors

Tensors have important applications in many scientific fields, such as signal processing, data analysis and mining. By applying Perron-Frobenius theory of nonnegative tensor to study eigenvalues, half-nonnegativity and principal subtensors of nonsingular M-tensor and general M-tensors, and some sufficient and necessary conditions of nonsingular M-tensors and some new properties of eigenvalues, half-nonnegativity and principal subtensor of general M-tensors are obtained. Based on these obtained results, the smallest eigenvalues of M-tensors are researched and new upper and lower bounds of the smallest eigenvalue for a special class of irreducible nonsingular M-tensors are given, and we prove that the bounds are better than that in the paper [J. He, T.Z. Huang, Inequalities for the M-tensors [J], J. Inequal. Appl.,2014,(2014)114]...