@article{Qi2025, 
author = {Qi Qi and Jun-e Feng},
title = {From DK-STP to a set of Lie bracket},
year = {2025},
journal = {Mathematical Modelling and Control},
volume = {5},
number = {4},
pages = {410-420},
keywords = {semi-tensor product, dimension keeping semi-tensor product, (anti) commutativity, Lie bracket, structure matrix},
url = {https://www.sciopen.com/article/10.3934/mmc.2025029},
doi = {10.3934/mmc.2025029},
abstract = {In this paper, semi-tensor product (STP) and related properties of dimension keeping semi-tensor product (DK-STP) are analyzed. The commutativity and anticommutativity of DK-STP are studied by means of matrix mapping, and sufficient conditions for both are obtained. The structure matrix of the Lie bracket of non-square matrices (NSM) is discussed, and some properties are derived. The correspondences between the special Lie subalgebras of square matrix and Lie subalgebras of NSM are discussed through a homomorphism.}
}