Abstract
In this paper, we propose two new classes of tensors: double B-tensors and quasi-double B-tensors, give some properties of double B-tensors and quasi-double B-tensors, discuss their relationships with B-tensors and positive definite tensors and show that even order symmetric double B-tensors and even order symmetric quasi-double B-tensors are positive definite. These give some checkable sufficient conditions for positive definiteness of tensors.
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