Abstract
Every matrix is permutation equivalent to a matrix that is the direct sum of indecomposable submatrices, and for such a decomposition the number and the dimensions of the summands are uniquely determined. By the tool, diagonal equivalence this combinatorial problem turns into an algebraic problem.
In memorial Elbert Walker
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Reference
Mader, A., Mutzbauer, O.: Double ordering of \((0,1)\)-matrices. Ars Combinatoria 61, 81–95 (2001)
Acknowledgements
Otto Mutzbauer was supported by grant MU 628/8-1 of the German Research Foundation DFG. Moreover, he would like to thank the Department of Mathematics at the University of Hawaii for the kind hospitality afforded him.
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Mader, A., Mutzbauer, O. (2020). Direct Decompositions of Matrices. In: Nguyen, H., Kreinovich, V. (eds) Algebraic Techniques and Their Use in Describing and Processing Uncertainty. Studies in Computational Intelligence, vol 878. Springer, Cham. https://doi.org/10.1007/978-3-030-38565-1_7
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DOI: https://doi.org/10.1007/978-3-030-38565-1_7
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