Czechoslovak Mathematical Journal, Vol. 72, No. 3, pp. 825-854, 2022


Additive decomposition of matrices under rank conditions and zero pattern constraints

Harm Bart, Torsten Ehrhardt

Received May 14, 2021.   Published online March 24, 2022.   OPEN ACCESS

Abstract:  This paper deals with additive decompositions $A=A_1+\cdots+A_p$ of a given matrix $A$, where the ranks of the summands $A_1,\ldots, A_p$ are prescribed and meet certain zero pattern requirements. The latter are formulated in terms of directed bipartite graphs.
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
Classification MSC:  15A21, 05C50, 15A03, 05C20


References:
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[2] H. Bart, T. Ehrhardt, B. Silbermann: Echelon type canonical forms in upper triangular matrix algebras. Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics. Operator Theory: Advances and Applications 259. Birkhäuser, Basel (2017), 79-124. DOI 10.1007/978-3-319-49182-0_8 | MR 3644514 | Zbl 1365.15014
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Affiliations:   Harm Bart (corresponding author), Econometric Institute, Erasmus University Rotterdam, Burgemeester Oudlaan 50, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands, e-mail: bart@ese.eur.nl; Torsten Ehrhardt, Mathematics Department, University of California, 1156, High St., Santa Cruz, CA-95064, USA, e-mail: tehrhard@ucsc.edu


 
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