Inverses of triangular matrices and bipartite graphs

To a given nonsingular triangular matrix A with entries from a ring, we associate a weighted bipartite graph G(A) and give a combinatorial description of the inverse of A by employing paths in G(A). Under a certain condition, nonsingular triangular matrices A such that A and A-1 have the same zero–n...

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Bibliographic Details
Published in:Linear algebra and its applications 2014-04, Vol.447, p.68-73
Main Authors: Bapat, R.B., Ghorbani, E.
Format: Article
Language:English
Subjects:
Bipartite graph
Outer inverse
Perfect matching
Tree
Triangular matrix
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Summary:To a given nonsingular triangular matrix A with entries from a ring, we associate a weighted bipartite graph G(A) and give a combinatorial description of the inverse of A by employing paths in G(A). Under a certain condition, nonsingular triangular matrices A such that A and A-1 have the same zero–nonzero pattern are characterized. A combinatorial construction is given to construct outer inverses of the adjacency matrix of a weighted tree.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2013.03.002