On some properties of the determinants of tensors |
| |
Authors: | Jia-Yu Shao Hai-Ying Shan Li Zhang |
| |
Institution: | Department of Mathematics, Tongji University, Shanghai 200092, China |
| |
Abstract: | We use the Hilbert?s Nullstellensatz (Hilbert?s Zero Point Theorem) to give a direct proof of the formula for the determinants of the products of tensors. By using this determinant formula and using tensor product to represent the transformations of the slices of tensors, we prove some basic properties of the determinants of tensors which are the generalizations of the corresponding properties of the determinants for matrices. We also study the determinants of tensors after two types of transposes. We use the permutational similarity of tensors to discuss the relation between weakly reducible tensors and the triangular block tensors, and give a canonical form of the weakly reducible tensors. |
| |
Keywords: | 15A18 15A69 |
本文献已被 ScienceDirect 等数据库收录! |
|