A new semi-tensor product of matrices

作者：Cheng, Daizhan^*; Liu, Zequn

来源：Control Theory and Technology, 2019, 17(1): 4-12.

DOI：10.1007/s11768-019-8161-2

• Equivalence relations
• Fundamental properties
• metric
• Quotient space
• Semi-tensor product
• Semi-tensor product of matrices
• Tensor products
• Vector space structures

A new matrix product, called the second semi-tensor product (STP-II) of matrices is proposed. It is similar to the classical semi-tensor product (STP-I). First, its fundamental properties are presented. Then, the equivalence relation caused by STP-II is obtained. Using this equivalence, a quotient space is also obtained. Finally, the vector space structure, the metric and the metric topology, the projection and subspaces, etc. of the quotient space are investigated in detail.

• 出版日期2019-2-1
• 单位中国科学院数学与系统科学研究院; 中国科学院大学