何建锋. 严格对角占优张量的子直和[J]. 华南师范大学学报(自然科学版), 2021, 53(3): 102-105. doi: 10.6054/j.jscnun.2021048
引用本文: 何建锋. 严格对角占优张量的子直和[J]. 华南师范大学学报(自然科学版), 2021, 53(3): 102-105. doi: 10.6054/j.jscnun.2021048
HE Jianfeng. The Subdirect Sum of Strictly Diagonally Dominant Tensors[J]. Journal of South China Normal University (Natural Science Edition), 2021, 53(3): 102-105. doi: 10.6054/j.jscnun.2021048
Citation: HE Jianfeng. The Subdirect Sum of Strictly Diagonally Dominant Tensors[J]. Journal of South China Normal University (Natural Science Edition), 2021, 53(3): 102-105. doi: 10.6054/j.jscnun.2021048

严格对角占优张量的子直和

The Subdirect Sum of Strictly Diagonally Dominant Tensors

  • 摘要: 根据张量与矩阵之间的联系,将方阵子直和及S-严格对角占优矩阵的概念推广到张量上,给出了张量子直和与S-严格对角占优型张量的定义,用分类讨论的方法证明2个严格对角占优张量的子直和仍然为严格对角占优张量,并讨论了S-严格对角占优型张量的情形,给出2个张量的子直和为S-严格对角占优型张量的条件.

     

    Abstract: The concept of subdirect sum of square matrices is extended to tensors according to the relation between matrix and tensor. The definitions of subdirect sum of tensors and S-strictly diagonally dominant tensors are given. It is proved, with the method of classification, that the subdirect sum of two strictly diagonally dominant tensors is also a strictly diagonally dominant tensor. Moreover, the condition ensuring that the subdirect sum of two tensors is the S-strictly diagonally dominant tensor is also given.

     

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