Study verifies inequalities on minimum H-eigenvalue in tensors, indicating mathematical properties of their products.
For the Fan product and the Hadamard product of tensors, we derive several inequalities for the minimum H-eigenvalue of \(Z\) -tensors. Using these inequalities, we verify whether the Hadamard product of a nonnegative tensor and a \(Z\) -tensor is an \(M\) -tensor and whether it is positive definite. Furthermore, several determinantal properties of the Hadamard product of an \(M\) -tensor and a nonnegative tensor are established.
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Guo et al. (2026) studied this question.
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