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This chapter investigates the properties of Boolean vector space over the Boolean field \(\mathcal {B}=\{0,1\}\) . Firstly, the dependence and independence of Boolean vectors are discussed. Secondly, the equivalence relation of Boolean vector group is presented. By means of the maximum independent Boolean vector group, the properties for the rank of Boolean vector group are explored. Thirdly, using the properties of extension group and homogeneous Boolean equation, the relationship between row rank and column rank of Boolean matrix is discussed. Finally, subspace and row (column) space of Boolean matrix are studied.

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Boolean Vector Space

  • 章节

  • 发表日期：

    2025年

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  • Haitao Li,
  • Xinrong Yang,
  • Wenrong Li

摘要

This chapter investigates the properties of Boolean vector space over the Boolean field \(\mathcal {B}=\{0,1\}\) . Firstly, the dependence and independence of Boolean vectors are discussed. Secondly, the equivalence relation of Boolean vector group is presented. By means of the maximum independent Boolean vector group, the properties for the rank of Boolean vector group are explored. Thirdly, using the properties of extension group and homogeneous Boolean equation, the relationship between row rank and column rank of Boolean matrix is discussed. Finally, subspace and row (column) space of Boolean matrix are studied.