We study irreducible tensors. the real and complex geometric simplicity of nonnegative First, we prove some basic conclusions. Based on the conclusions, the real geometric simplicity of the spectral radius of an even-...We study irreducible tensors. the real and complex geometric simplicity of nonnegative First, we prove some basic conclusions. Based on the conclusions, the real geometric simplicity of the spectral radius of an even- order nonnegative irreducible tensor is proved. For an odd-order nonnegative irreducible tensor, sufficient conditions are investigated to ensure the spectral radius to be real geometrically simple. Furthermore, the complex geometric simplicity of nonnegative irreducible tensors is also studied.展开更多
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
文摘We study irreducible tensors. the real and complex geometric simplicity of nonnegative First, we prove some basic conclusions. Based on the conclusions, the real geometric simplicity of the spectral radius of an even- order nonnegative irreducible tensor is proved. For an odd-order nonnegative irreducible tensor, sufficient conditions are investigated to ensure the spectral radius to be real geometrically simple. Furthermore, the complex geometric simplicity of nonnegative irreducible tensors is also studied.
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.
