Obtaining bounds on the two norm of a matrix from the splitting lemma.
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...
On a conjecture regarding characteristic polynomial of a matrix pair.
On a Theorem of Gersgorin.
On Bauer's Generalized Gershgorin Discs.
On condition numbers of a nondefective multiple eigenvalue.
On convexity, the Weyl group and the Iwasawa decomposition
On elementary symmetric functions of the eigenvalues of the sum and product of normal matrices
On Geršgorin-type problems and ovals of cassini.
On graphs with the largest Laplacian index
Let be a connected simple graph on vertices. The Laplacian index of , namely, the greatest Laplacian eigenvalue of , is well known to be bounded above by . In this paper, we give structural characterizations for graphs with the largest Laplacian index . Regular graphs, Hamiltonian graphs and planar graphs with the largest Laplacian index are investigated. We present a necessary and sufficient condition on and for the existence of a -regular graph of order with the largest Laplacian...
On Matrix Norms and Logarithmic Norms.
On spaces of matrices with a bounded number of eigenvalues.
On spectra of expansion graphs and matrix polynomials. II.
On spectral variations under bounded real matrix perturbations.
On stability of parametrized families of polynomials and matrices.
On the angles between certain arithmetically defined subspaces of
If and are two families of unitary bases for , and is a fixed number, let and be subspaces of spanned by vectors in and respectively. We study the angle between and as goes to infinity. We show that when and arise in certain arithmetically defined families, the angles between and may either tend to or be bounded away from zero, depending on the behavior of an associated eigenvalue problem.
On the arguments of proper values of normal and unitary transformations
On the -stability problem for real matrices
Vengono discusse delle condizioni sufficienti affinchè una matrice reale delle dimensioni sia diagonalmente (o -) stabile. Esse includono delle ipotesi geometriche (condizioni degli ortanti), e un criterio che generalizza un criterio di Carlson. Inoltre si discute la -stabilità robusta per le matrici reali delle dimensioni
On the diagonals of integral matrices
On the effect of the perturbation of a nonnegative matrix on its Perron eigenvector