On C-tensor and its application to eigenvalue localization.

The notions of C-tensor, C0-tensor and C ¯ -tensor are introduced first. Different necessary and sufficient conditions for a tensor to be a C-tensor, C0-tensor and C ¯ -tensor are provided. We next show that the sum of two C-tensors (C0-tensors) is a C-tensor (C0-tensor) while the Hadamard product of two C-tensors (C0-tensors) is not a C-tensor (C0-tensor). We also present a result that illustrates the Hadamard product of two C-tensor is again a C-tensor under some sufficient conditions. As an application of these classes of tensors, an exclusion interval for the real eigenvalues of a real tensor is proposed. Finally, we provide a necessary and sufficient condition for the exclusion interval to be nonempty. [ABSTRACT FROM AUTHOR]