Some applications of semitensor product of matrices in algebra

摘要

A review on semitensor product (STP) of matrices is given. It is a generalization of the conventional matrix product for the case when the dimensions of the factor matrices do not satisfy the requirement. Using it, we investigate some structure-related properties of algebras. First, we consider when an algebra is a Lie algebra. The result reveals the topological structure of all finite-dimensional Lie algebras as the variety of a set of polynomial equations. Then we investigate the invertibility of algebras. Invertibility condition is expressed via STP. Finally, the tensor product of algebras is investigated. (c) 2006 Elsevier Ltd. All rights reserved.