As a new matrix product, semi-tensor product of matrices has attracted more and more attention and participation from domestic and international academic
society, and it has been applied to more and more research topics. The purpose of this paper is to analyze the fundamental principle of semi-tensor product, and to explain the reason for the emergence and existence of the semi-tensor product. Unlike the existing surveys, this paper does not intend to introduce what applications the semi- tensor product has been used to. Instead, we want to explore what kind of problems the semi-tensor product might be used according to the essence of semi-tensor product. Such observation could help us to dig out unknown possible further applications of semi-tensor product.