Axiomatized semi-tensor product of matrices
CHENG Dai-zhan
ZHAO Rong
FENG Jun-e
Abstract：An axiomatic framework is provided for the semi-tensor product(STP)of matrices,which consists of three kinds of STPs:matrix-matrix STP,matrix-vector STP and vector-vector STP.First,several commonly used STPs are surveyed with their basic properties and applications.Then,a newly appearing STP,called the dimension keeping STP,is introduced.The dimension keeping STP is a multi-functional STP,which can realize the functions of the matrix-matrix STP,matrix-vector STP,and vector-vector STP simultaneously.Finally,this paper also briefly introduces some algebraic properties brought by the dimension keeping STP,including Cayley-Hamilton theory of non-square matrices,eigenvalue and eigenvector of non-square matrices.
Keywords：axiomatized semi-tensor producthypermatrixdimension keeping semi-tensor productCayley-Hamilton theory of non-square matrices
Publication Date：2024-07-28
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：9( 1172-1180 )