@article{Cheng2021, 
author = {Daizhan Cheng and Ying Li and Jun-e Feng and Jianli Zhao},
title = {On numerical/non-numerical algebra: Semi-tensor product method},
year = {2021},
journal = {Mathematical Modelling and Control},
volume = {1},
number = {1},
pages = {1-11},
keywords = {numerical (non-numerical) algebra, numeralization (dis-numeralization), semi-tensor product (STP) of matrices, commutative quaternion},
url = {https://www.sciopen.com/article/10.3934/mmc.2021001},
doi = {10.3934/mmc.2021001},
abstract = {A kind of algebra, called numerical algebra, is proposed and investigated. As its opponent, non-numerical algebra is also defined. The numeralization and dis-numeralization, which convert non-numerical algebra to numerical algebra and vise versa, are considered. Product structure matrix (PSM) of a finite dimensional algebra is constructed. Using PSM, some fundamental properties of finite dimensional algebras are obtained. Then a necessary and sufficient condition for a numerical algebra to be a field is presented. Finally, the invertibility of Segre (commutative) quaternion and some related properties of matrices over Segre quaternion are investigated.}
}