MB-tensors and MB0-tensors
arXiv:1411.6316
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Provides a theoretical extension and proof for tensor positivity, relevant to researchers in multilinear algebra and tensor analysis.
The paper introduces MB and MB0 tensors, generalizing B and quasi-double B tensors, and proves that even-order symmetric MB and MB0 tensors are positive (semi-)definite, resolving a conjecture by Li and Li.
The class of MB(MB0)-tensors, which is a generation of B(B0)-tensors and quasi-double B(B0)-tensors, is proposed. And we prove that an even order symmetric MB(MB0)-tensor is positive (semi-)definite. This provides a positive answer for the conjecture in Li and Li's paper [15] that an even order symmetric quasi-double B0-tensor is positive semi-definite.