Inverses of Boolean matrices

D. E. Rutherford

doi:10.1017/S2040618500034705

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This note is concerned with square matrices, denoted by capital letters, whose elements belong to aBoolean algebra with null element 0 and all element 1. Such matrices, which have important applicationsin the theory of electric circuits, can be compounded in the three following ways.

References

REFERENCES

1.Wedderburn, J. H. M., Boolean linear associative algebra, Ann. of Math. 35 (1934), 185–194.CrossRef Google Scholar

2.Luce, R. D., A note on Boolean matrix theory, Proc. Amer. Math. Soc. 3 (1952), 382–388.Google Scholar

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Blyth, T. S. 1964. Residuation theory and Boolean matrices. Proceedings of the Glasgow Mathematical Association, Vol. 6, Issue. 4, p. 185.

Rutherford, D. E. 1965. IX.—Orthogonal Boolean Matrices. Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences, Vol. 67, Issue. 2, p. 126.

Blyth, T. S. 1965. ⋏-distributive Boolean matrices. Proceedings of the Glasgow Mathematical Association, Vol. 7, Issue. 2, p. 93.

Simões Pereira, J. M. S. 1968. Boolean Permanents, Permutation Graphs and Products. SIAM Journal on Applied Mathematics, Vol. 16, Issue. 6, p. 1251.

Bevis, J. H. 1969. Matrices over orthomodular lattices. Glasgow Mathematical Journal, Vol. 10, Issue. 1, p. 55.

Chesley, D. S. and Bevis, J. H. 1969. X.—Determinants for Matrices over Lattices. Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences, Vol. 68, Issue. 2, p. 138.

Bevis, J. H. and Martin, C. K. 1969. Residuation theory and matrix multiplication on orthomodular lattices. Glasgow Mathematical Journal, Vol. 10, Issue. 1, p. 60.

Butler, Kim Ki-Hang 1974. Combinatorial Mathematics. Vol. 403, Issue. , p. 18.

Prasada Rao, P.S.S.N.V. and Bhaskara Rao, K.P.S. 1975. On generalized inverses of Boolean Matrices. Linear Algebra and its Applications, Vol. 11, Issue. 2, p. 135.

Kim, Ki Hang and Roush, Fred W. 1978. Inverses of Boolean matrices. Linear Algebra and its Applications, Vol. 22, Issue. , p. 247.

Skornyakov, L. A. 1987. Invertible matrices over distributive lattices. Siberian Mathematical Journal, Vol. 27, Issue. 2, p. 289.

Van Mechelen, Iven De Boeck, Paul and Rosenberg, Seymour 1995. The conjunctive model of hierarchical classes. Psychometrika, Vol. 60, Issue. 4, p. 505.

Il’in, S. N. 1998. Invertibility of matrices over ordered algebraic systems. Siberian Mathematical Journal, Vol. 39, Issue. 3, p. 476.

Ceulemans, Eva and Van Mechelen, Iven 2003. Uniqueness of N-way N-mode hierarchical classes models. Journal of Mathematical Psychology, Vol. 47, Issue. 3, p. 259.

Marenich, E. E. and Kumarov, V. G. 2007. Inversion of matrices over a pseudocomplemented lattice. Journal of Mathematical Sciences, Vol. 144, Issue. 2, p. 3968.

Poplavski, V. B. 2008. On cofactor expansion of determinants of Boolean matrices. Journal of Mathematical Sciences, Vol. 155, Issue. 6, p. 932.

Song, Seok-Zun Kang, Kyung-Tae Beasley, LeRoy B. and Sze, Nung-Sing 2008. Regular matrices and their strong preservers over semirings. Linear Algebra and its Applications, Vol. 429, Issue. 1, p. 209.

Pattison, Philippa 2009. Encyclopedia of Complexity and Systems Science. p. 8291.

Gudder, Stan and Latrémolière, Frédéric 2009. Boolean inner-product spaces and Boolean matrices. Linear Algebra and its Applications, Vol. 431, Issue. 1-2, p. 274.

Zhao, Shan and Wang, Xue-ping 2010. Invertible matrices and semilinear spaces over commutative semirings. Information Sciences, Vol. 180, Issue. 24, p. 5115.

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Inverses of Boolean matrices

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