矩阵的半张量积: 一个便捷的新工具
摘要
Semi-tensor product of matrices is a new matrix product. It generalizes the conventional matrix product to the case when the column number of the leading factor matrix does not equal to the row number of the following factor matrix. The generalized product keeps all major properties of the conventional matrix product unchanged. After introducing its history, definitions and main properties, this survey is emphasized on its applications to the analysis and control of dynamic systems, which mainly contain the followings: (1) semi-tensor product approach to nonlinear dynamic systems; (2) structure analysis and control of Boolean networks; (3) some other applications. Finally, a prediction for the potential applications of semi-tensor product is provided.