Nonexistence results for Hadamard-like matrices.
Permanents of Hessenberg -matrices revisited.
Short score certificates for upset tournaments.
Sign-consistency and solvability of constrained linear systems.
Sign patterns that require a positive or nonnegative left inverse.
Tight bounds on the algebraic connectivity of a balanced binary tree.
Non-existence of full ray nonsingular matrices.
Even and odd tournament matrices with minimum rank over finite fields.
Proceedings of the 2004 workshop on directions in combinatorial matrix theory, Banff, Canada, May 7--8, 2004.
On determining minimal spectrally arbitrary patterns.
Generating potentially nilpotent full sign patterns.
On a bound on algebraic connectivity: the case of equality
In a recent paper the authors proposed a lower bound on , where , , is an eigenvalue of a transition matrix of an ergodic Markov chain. The bound, which involved the group inverse of , was derived from a more general bound, due to Bauer, Deutsch, and Stoer, on the eigenvalues of a stochastic matrix other than its constant row sum. Here we adapt the bound to give a lower bound on the algebraic connectivity of an undirected graph, but principally consider the case of equality in the bound when...
Bounds on the subdominant eigenvalue involving group inverses with applications to graphs
Let be an symmetric, irreducible, and nonnegative matrix whose eigenvalues are . In this paper we derive several lower and upper bounds, in particular on and , but also, indirectly, on . The bounds are in terms of the diagonal entries of the group generalized inverse, , of the singular and irreducible M-matrix . Our starting point is a spectral resolution for . We consider the case of equality in some of these inequalities and we apply our results to the algebraic connectivity of undirected...
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