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） d...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.展开更多
It is known that every tensor has an associated semi-symmetric tensor.The purpose of this paper is to investigate the shared properties of a tensor and its semi-symmetric form.In particular,a corresponding semi-symmet...It is known that every tensor has an associated semi-symmetric tensor.The purpose of this paper is to investigate the shared properties of a tensor and its semi-symmetric form.In particular,a corresponding semi-symmetric tensor has smaller Frobenius norm under some conditions and can be used to get smaller bounds for eigenvalues and solutions of dynamical systems and tensor complementarity problems.In addition,every tensor has the same eigenvalues as its corresponding semi-symmetric form,also a corresponding semi-symmetric tensor inherits properties like being circulant,Toeplitz,Z-tensor,M-tensor,H-tensor and some others.Also,there are a two-way connection for properties like being positive definite,P-tensor,semi-positive,primitive and several others.展开更多
文摘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.
文摘It is known that every tensor has an associated semi-symmetric tensor.The purpose of this paper is to investigate the shared properties of a tensor and its semi-symmetric form.In particular,a corresponding semi-symmetric tensor has smaller Frobenius norm under some conditions and can be used to get smaller bounds for eigenvalues and solutions of dynamical systems and tensor complementarity problems.In addition,every tensor has the same eigenvalues as its corresponding semi-symmetric form,also a corresponding semi-symmetric tensor inherits properties like being circulant,Toeplitz,Z-tensor,M-tensor,H-tensor and some others.Also,there are a two-way connection for properties like being positive definite,P-tensor,semi-positive,primitive and several others.
