A new definition of geometric multiplicity of eigenvalues of tensors and some results based on it

作者：Li, Yiyong; Yang, Qingzhi^*; Yang, Yuning

来源：Frontiers of Mathematics in China, 2015, 10(5): 1123-1146.

DOI：10.1007/s11464-015-0412-z

• Irreducible tensor
• Perron-Frobenius theorem
• geometrically simple

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(A) have the same geometric multiplicity. We also prove that two-dimensional nonnegative tensors' geometric multiplicity of eigenvalues is equal to algebraic multiplicity of eigenvalues.

• 出版日期2015-10
• 单位南开大学