We give a new definition of geometric multiplicity of eigenvalues of tensors, and based on this, we study the geometric and algebraic multiplicity of irreducible tensors＇ eigenvalues. We get the result that the eigen...We give a new definition of geometric multiplicity of eigenvalues of tensors, and based on this, we study the geometric and algebraic multiplicity of irreducible tensors＇ eigenvalues. We get the result that the eigenvalues with modulus p have the same geometric multiplicity. We also prove that two- dimensional nonnegative tensors＇ geometric multiplicity of eigenvalues is equal to algebraic multiplicity of eigenvalues.展开更多
基金Acknowledgements The authors are grateful to Mr. Xi He and Mr. Zhongming Chen for their helpful discussion. And the authors would like to thank the reviewers for their suggestions to improve the presentation of the paper. This work was supported in part by the National Natural Science Foundation of China （Grant No. 11271206） and the Natural Science Foundation of Tianjin （Grant No. 12JCYBJC31200）.
文摘We give a new definition of geometric multiplicity of eigenvalues of tensors, and based on this, we study the geometric and algebraic multiplicity of irreducible tensors＇ eigenvalues. We get the result that the eigenvalues with modulus p have the same geometric multiplicity. We also prove that two- dimensional nonnegative tensors＇ geometric multiplicity of eigenvalues is equal to algebraic multiplicity of eigenvalues.
