Related papers: Spectrally arbitrary pattern extensions
We compute spectra of large stochastic matrices $W$, defined on sparse random graphs, where edges $(i,j)$ of the graph are given positive random weights $W_{ij}>0$ in such a fashion that column sums are normalized to one. We compute spectra…
This paper deals with structural controllability of leader-follower networks. The system matrix defining the network dynamics is a pattern matrix in which a priori given entries are equal to zero, while the remaining entries take nonzero…
A graph is called $k$-extendable if each $k$-matching can be extended to a perfect matching. We give spectral conditions for the $k$-extendability of graphs and bipartite graphs using Tutte-type and Hall-type structural characterizations.…
The bispectral problem is motivated by an effort to understand and extend a remarkable phenomenon in Fourier analysis on the real line: the operator of time-and-band limiting is an integral operator admitting a second-order differential…
A sign pattern is a matrix whose entries belong to the set $\{+,-,0\}$. A sign pattern requires a unique inertia if every real matrix in its qualitative class has the same inertia. Symmetric tree sign patterns requiring a unique inertia has…
Patterns on numerical semigroups are multivariate linear polynomials, and they are said to be admissible if there exists a numerical semigroup such that evaluated at any nonincreasing sequence of elements of the semigroup gives integers…
For a real matrix $M$, we denote by $sp(M)$ the spectrum of $M$ and by $\left \vert M\right \vert $ its absolute value, that is the matrix obtained from $M$ by replacing each entry of $M$ by its absolute value. Let $A$ be a nonnegative real…
In this paper we investigate the spectral expansion for the asymptotically spectral differential operators generated in all real line by ordinary differential expression of arbitrary order with periodic matrix-valued coefficients
I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…
Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration"…
Any associative bilinear multiplication on the set of n-by-n matrices over some field of characteristic not two, that makes the same vectors orthogonal and has the same trace as ordinary matrix multiplication, must be ordinary matrix…
A spectral faux tree with respect to a given matrix is a graph which is not a tree but is cospectral with a tree for the given matrix. We consider the existence of spectral faux trees for several matrices, with emphasis on constructions.…
Spectral decomposition of matrices is a recurring and important task in applied mathematics, physics and engineering. Many application problems require the consideration of matrices of size three with spectral decomposition over the real…
Even though image signals are typically acquired on a regular two dimensional grid, there exist many scenarios where non-regular sampling is possible. Non-regular sampling can remove aliasing. In terms of the non-regular sampling patterns,…
We take on a Random Matrix theory viewpoint to study the spectrum of certain reversible Markov chains in random environment. As the number of states tends to infinity, we consider the global behavior of the spectrum, and the local behavior…
The study of spectral graph determination is a fascinating area of research in spectral graph theory and algebraic combinatorics. This field focuses on examining the spectral characterization of various classes of graphs, developing methods…
We describe, in a very explicit way, a method for determining the spectra and bases of all the corresponding eigenspaces of arbitrary lifts of graphs (regular or not).
We compute explicitly (modulo solutions of certain algebraic equations) the spectra of infinite graphs obtained by attaching one or several infinite paths to some vertices of certain finite graphs. The main result concerns a canonical form…
The isospectral reduction of matrix, which is closely related to its Schur complement, allows to reduce the size of a matrix while maintaining its eigenvalues up to a known set. Here we generalize this procedure by increasing the number of…
We develop a framework for nonstandard analysis that gives foundations to the interplay between external and internal iterations of the star map, and we present a few examples to show the strength and flexibility of such a nonstandard…