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This paper investigates the algebraic relationships between the dimension-keeping semi-tensor product of matrices (DK-STP) and the semi-tensor product of matrices (STP). Firstly, the definitions of five types of STPs and the type-I DK-STP are given. Secondly, the fundamental properties of the type-I DK-STP are introduced. Thirdly, the algebraic relationships between the type-I DK-STP and these five types of STPs are explored respectively. Finally, the DK-STP is generalized, and the algebraic relationships between the right DK-STP and the right STPs are discussed.

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The Algebraic Relationships Between DK-STP and STP

  • 会议论文

  • 发表日期：

    2026年

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  • Qi An,
  • Changxi Li,
  • Jun-e Feng

摘要

This paper investigates the algebraic relationships between the dimension-keeping semi-tensor product of matrices (DK-STP) and the semi-tensor product of matrices (STP). Firstly, the definitions of five types of STPs and the type-I DK-STP are given. Secondly, the fundamental properties of the type-I DK-STP are introduced. Thirdly, the algebraic relationships between the type-I DK-STP and these five types of STPs are explored respectively. Finally, the DK-STP is generalized, and the algebraic relationships between the right DK-STP and the right STPs are discussed.