The tensor eigenproblem has many important applications. This paper studies the eigenproblem for tensor and tensor transposition,and proves that the mode-p, eigenpair of tensor is the same as the mode-I eigenpair of p-transposition of tensor. It is illustrated by examples that the mode-z eigenvalue of tensor is not necessarily equal to that of p-transposition of tensor,and the eigenvectors corresponding to the mode-I eigenvalueμ, and the mode-j eigenvalue μ, are not orthogonal when μ,≠μ Therefore,the results show that the properties of eigenvalues of matrix can not be completely extended to tensor. Based on this conclusion, this paper gives a condition that the index vector p should satisfy when the mode-z eigenpair of tensor is equal to that of the p-transposition of tensor.%研究了张量与张量转置的特征值问题,证明了张量的mode-p,特征对与张量p-转置的mode-i特征对是相同的,通过例子说明了张量与张量p-转置的mode-i特征值不一定相等,当mode-i特征值μ1和mode-j特征值μ1不相等时,对应的特征向量也不一定正交.从而说明了矩阵特征值的性质并不能完全推广到张量情形.此外,还给出了张量与张量p-转置的mode-i特征对相等时指标向量p需要满足的条件.
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