Abstract
Several authors in recent years investigated the properties of the Moore-Penrose inverse of an arbitrary Boolean relation matrix. The concept of a Moore-Penrose inverse for Boolean relation matrices was discussed first by Rutherford [11] and then independently discovered by Markowsky [8], Plemmons [10], and the author ([3] and [4]). It is natural to inquire whether or not the Moore-Penrose inverse is unique, if it exists. In this paper, the properties of unique Moore-Penrose inverse of an arbitrary Boolean relation matrix are examined in connection with partial order relation and three computational methods for the unique Moore-Penrose inverse for an arbitrary Boolean relation matrix is developed.
Keywords
- Generalize Inverse
- Partial Order Relation
- Nonsingular Matrice
- Boolean Matrice
- Penrose Inverse
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© 1974 Springer-Verlag
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Butler, K.KH. (1974). A moore-penrose inverse for boolean relation matrices. In: Holton, D.A. (eds) Combinatorial Mathematics. Lecture Notes in Mathematics, vol 403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0057372
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DOI: https://doi.org/10.1007/BFb0057372
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