2016/08/04 by Kuize Zhang, Zhang, Kuize
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1608.01578
openalex publication_date 2016/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The semi-tensor product (STP) of matrices which was proposed by Daizhan Cheng in 2001 [2], is a natural generalization of the standard matrix product and well defined at every two finite-dimensional matrices. In 2016, Cheng proposed a new concept of semi-tensor addition (STA) which is a natural generalization of the standard matrix addition and well defined at every two finite-dimensional matrices with the same ratio between the numbers of rows and columns [1]. In addition, an identify equivalence relation between matrices was defined in [1], STP and STA were proved valid for the corresponding identify equivalence classes, and the corresponding quotient space was endowed with an algebraic structure and a manifold structure. In this follow-up paper, we give a new concise basis for the quotient space, which also shows that the Lie algebra corresponding to the quotient space is of countably infinite dimension.