Inverses of triangular matrices and bipartite graphs

2013/03/09 by Ravindra Bapat, Bapat, Ravindra, Ebrahim Ghorbani +1 · 1 citation
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1303.2177

9 pages

arxiv created 2013/03/09 · arxiv updated 2013/03/12

Abstract

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.

Cited by

• On generalized inverses of matrices associated with certain graph classes

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