Inverses of triangular matrices and bipartite graphs
Combinatorics
2013-03-12 v1
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.
Cite
@article{arxiv.1303.2177,
title = {Inverses of triangular matrices and bipartite graphs},
author = {Ravindra Bapat and Ebrahim Ghorbani},
journal= {arXiv preprint arXiv:1303.2177},
year = {2013}
}
Comments
9 pages