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Intervals of certain classes of Z-matrices

M. Rajesh KannanK.C. Sivakumar — 2014

Discussiones Mathematicae - General Algebra and Applications

Let A and B be M-matrices satisfying A ≤ B and J = [A,B] be the set of all matrices C such that A ≤ C ≤ B, where the order is component wise. It is rather well known that if A is an M-matrix and B is an invertible M-matrix and A ≤ B, then aA + bB is an invertible M-matrix for all a,b > 0. In this article, we present an elementary proof of a stronger version of this result and study corresponding results for certain other classes as well.

Eigenvalue bounds for some classes of matrices associated with graphs

Ranjit MehatariM. Rajesh Kannan — 2021

Czechoslovak Mathematical Journal

For a given complex square matrix A with constant row sum, we establish two new eigenvalue inclusion sets. Using these bounds, first, we derive bounds for the second largest and the smallest eigenvalues of adjacency matrices of k -regular graphs. Then we establish some bounds for the second largest and the smallest eigenvalues of the normalized adjacency matrices of graphs and the second smallest and the largest eigenvalues of the Laplacian matrices of graphs. The sharpness of these bounds is verified...

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