We present a method to linearize, without approximation, specific class of eigenvalue problems with eigenvector nonlinearities (NEPv), where the are expressed by scalar functions that defined quotient linear eigenvector. The exact linearization relies on an equivalent multiparameter problem (MEP) contains solutions NEPv. Due characterization MEPs in terms generalized this provides direct way co...

The recursively-constructed family of Mandelbrot matrices $M_n$ for $n=1$, $2$, $\ldots$ have nonnegative entries (indeed just $0$ and $1$, so each can be called a binary matrix) eigenvalues whose negatives $-\lambda = c$ give periodic orbits under the iteration, namely $z_k z_{k-1}^2+c$ with $z_0=0$, are thus contained in set. By Perron--Frobenius theorem, dominant real positive eigenvalue, wh...

We introduce a technique for analyzing the temporal evolution of the salience of participants in a discussion. Our method can dynamically track how the relative importance of speakers evolve over time using graph based techniques. Speaker salience is computed based on the eigenvector centrality in a graph representation of participants in a discussion. Two participants in a discussion are linke...

This paper gives double angle theorems that bound the change in an invariant subspace of an indeenite Hermitian matrix in the graded form H = D AD subject to a perturbation H ! e H = D (A + A)D. These theorems extend recent results on a deenite Hermitian matrix in the graded form (Linear Algebra Appl., 311 (2000), 45{60) but the bounds here are more complicated in that they depend on not only r...

An incredible number of centrality indices has been proposed to date (Todeschini & Consonni, 2009). Four of them, however, can be considered prototypical because they operationalize distinct concepts of centrality and together cover the bulk of analyses and empirical uses: degree, closeness, betweenness, and eigenvector centrality. In teaching any mathematical science, it is instructive to cons...

The superscript H refers to the Hermitian transpose, which includes transposition and complex conjugation. That is, for any matrix A, AH = AT . An eigenvector of A, as defined above, is sometimes called a right eigenvector of A, to distinguish from a left eigenvector. It can be seen that if y is a left eigenvector of A with eigenvalue λ, then y is also a right eigenvector of AH , with eigenvalu...