Some classes of nonsingular tensors and application

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