Abstract
This paper deals with additive decompositions A = A1 + … + Ap of a given matrix A, where the ranks of the summands A1, …, Ap are prescribed and meet certain zero pattern requirements. The latter are formulated in terms of directed bipartite graphs.
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Dedicated to our friend and colleague Bernd Silbermann on the occasion of his 80-th birthday, with admiration
Torsten Ehrhardt was supported in parts by the Simons Foundation Collaboration Grant # 525111. Open access funding provided by Erasmus University.
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Bart, H., Ehrhardt, T. Additive decomposition of matrices under rank conditions and zero pattern constraints. Czech Math J 72, 825–854 (2022). https://doi.org/10.21136/CMJ.2022.0185-21
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DOI: https://doi.org/10.21136/CMJ.2022.0185-21
Keywords
- additive decomposition
- rank constraint
- zero pattern constraint
- directed bipartite graph
- L-free directed bipartite graph
- permutation L-free directed bipartite graph
- Bell number
- Stirling partition number