This chapter provides a basic introduction to the semi-tensor product of matrices. We will emphasize concepts, geometric interpretations, and some fundamental properties. All proofs are omitted as we refer to Cheng and Qi (Semi-tensor Product of Matrices—Theory and Applications, Science Press, Beijing, 2007) for them. The theory of the semi-tensor product consists mainly of two parts: algebraic calculation and differential calculation. A survey can be found in Cheng (Proc. 4th International Congress of Chinese Mathematicians, pp. 641–668, Higher Edu. Press, Int. Press, Hangzhou, 2007). This book involves only the first part, which is introduced in this chapter. We refer to Mei et al. (Semi-tensor Product Approach to Transient Analysis of Power Systems, Tsinghua Univ. Press, Beijing, 2010) for some applications of the semi-tensor product to power systems, where the second part (differential calculation) is mainly used.

Daizhan Cheng

Semi-tensor Product of Matrices

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