Further results on B-tensors with application to location of real eigenvalues

Abstract

We give a further study on B-tensors and introduce doubly B-tensors that contain B-tensors. We show that they have similar properties, including their decompositions and strong relationship with strictly (doubly) diagonally dominated tensors. As an application, the properties of B-tensors are used to localize real eigenvalues of some tensors, which would be very useful in verifying the positive semi-definiteness of a tensor.

Key words： B-tensors; doubly B-tensors; eigenvalues of tensors; decomposition of B-tensors; decomposition of doubly B-tensors; positive semi-definiteness

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