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| Contracted product of hypermatrices via STP of matrices |
| DaizhanCheng1,MinMeng2,XiaoZhang1,3,ZhengpingJi1,4 |
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| (1 Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;2 Department of Control Science and Engineering, School of Electronics and Information Engineering, Tongji University, Shanghai 201210, China;3 National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences, Beijing 100190, China;4 School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100149, China) |
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| 摘要: |
| An equivalent definition of hypermatrices is introduced. The matrix expression of hypermatrices is proposed. Using permutation matrices, the conversion between different matrix expressions is revealed. The various kinds of contracted products of hypermatrices are realized by semi-tensor products (STP) of matrices via matrix expressions of hypermatrices. |
| 关键词: d-hypermatrix · Matrix expression · Permutation matrices · Contracted product · Semi-tensor product (STP) |
| DOI：https://doi.org/10.1007/s11768-023-00155-w |
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| 基金项目:This work was supported partly by the National Natural Science Foundation of China (NSFC) (Nos. 62073315, 62103305), the Shanghai Pujiang Program (No. 21PJ 1413100), and China Postdoctoral Science Foundation (Nos. 2021M703423, 2022T150686). |
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| Contracted product of hypermatrices via STP of matrices |
| Daizhan Cheng1,Min Meng2,Xiao Zhang1,3,Zhengping Ji1,4 |
| (1 Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;2 Department of Control Science and Engineering, School of Electronics and Information Engineering, Tongji University, Shanghai 201210, China;3 National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences, Beijing 100190, China;4 School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100149, China) |
| Abstract: |
| An equivalent definition of hypermatrices is introduced. The matrix expression of hypermatrices is proposed. Using permutation matrices, the conversion between different matrix expressions is revealed. The various kinds of contracted products of hypermatrices are realized by semi-tensor products (STP) of matrices via matrix expressions of hypermatrices. |
| Key words: d-hypermatrix · Matrix expression · Permutation matrices · Contracted product · Semi-tensor product (STP) |
