The Subdirect Sum of Strictly Diagonally Dominant Tensors

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.