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The notions of  C -tensor,  C0 -tensor and-tensor are introduced first. Different necessary and sufficient conditions for a tensor to be a  C -tensor,  C0 -tensor and-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.

On C -tensor and its application to eigenvalue localization