Abstract
The concept of C π R -matrix is extended to C π R -tensor, which also generalizes the concept of C-tensor. A necessary and sufficient condition for a tensor to be a C π R -tensor is provided. We analyse decompositions of C π R -tensors and prove that C π R -tensors are nonsingular. Positive linear combinations and Hadamard product of two C π R -tensors are also discussed. Finally, some properties of B π R -tensor are given to localize real eigenvalues of a tensor.
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