Holomorphic Relative Inverses of Operator Valued Functions.
This paper deals with additive decompositions of a given matrix , where the ranks of the summands are prescribed and meet certain zero pattern requirements. The latter are formulated in terms of directed bipartite graphs.
For a block upper triangular matrix, a necessary and sufficient condition has been given to let it be the sum of block upper rectangular matrices satisfying certain rank constraints; see H. Bart, A. P. M. Wagelmans (2000). The proof involves elements from integer programming and employs Farkas' lemma. The algebra of block upper triangular matrices can be viewed as a matrix algebra determined by a pattern of zeros. The present note is concerned with the question whether the decomposition result referred...
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