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Additive decomposition of matrices under rank conditions and zero pattern constraints. (English) Zbl 07584105

Summary: 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.

MSC:

15A21 Canonical forms, reductions, classification
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
15A03 Vector spaces, linear dependence, rank, lineability
05C20 Directed graphs (digraphs), tournaments
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References:

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