  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.
