Abstract
Two new S-type inclusion theorems for the M-eigenvalues of a 4th-order partially symmetric tensor are established. These inclusion theorems provide upper bounds for the M-spectral radius of 4th-order partially symmetric tensors. Finally, the M-positive definiteness for 4th-order partially symmetric tensors are further studied and two sufficient conditions are also presented based on the two new S-type M-eigenvalue inclusion theorems.
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