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This chapter investigates the existence and calculation of generalized inverse for Boolean matrix over the Boolean field \(\mathcal {B}=\{0,1\}\) . As two special types of Boolean matrices, elementary Boolean matrix and full-rank Boolean matrix play an important role in the study of general Boolean matrices, which are firstly explored by introducing the elementary transformations and equivalence relation of Boolean matrices. After that, by resorting to the Boolean matrix decomposition theory, the existence of generalized inverse of general Boolean matrix is studied. Finally, two algorithms are established for deriving the generalized inverse of general Boolean matrix based on the properties of decomposable Boolean matrix and the canonical form of Boolean matrix, respectively.

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Generalized Inverse of Boolean Matrix

  • 章节

  • 发表日期：

    2025年

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  • Haitao Li,
  • Xinrong Yang,
  • Wenrong Li

摘要

This chapter investigates the existence and calculation of generalized inverse for Boolean matrix over the Boolean field \(\mathcal {B}=\{0,1\}\) . As two special types of Boolean matrices, elementary Boolean matrix and full-rank Boolean matrix play an important role in the study of general Boolean matrices, which are firstly explored by introducing the elementary transformations and equivalence relation of Boolean matrices. After that, by resorting to the Boolean matrix decomposition theory, the existence of generalized inverse of general Boolean matrix is studied. Finally, two algorithms are established for deriving the generalized inverse of general Boolean matrix based on the properties of decomposable Boolean matrix and the canonical form of Boolean matrix, respectively.