相关论文: Spectral Properties of a Binomial Matrix
We explore how the combinatorial arrangement of prescribed zeros in a matrix affects the possible eigenvalues that the matrix can obtain. We demonstrate that there are inertially arbitrary patterns having a digraph with no 2-cycle, unlike…
We characterize the eigenvalues and eigenvectors of a class of complex valued tridiagonal $n$ by $n$ matrices subject to arbitrary boundary conditions, i.e. with arbitrary elements on the first and last rows of the matrix. %By boundary…
This paper explores the Harmonic matrix $MH(G)$ associated with a simple graph $ G $, where each entry corresponds to $ \frac{2}{d_i + d_j} $ for adjacent vertices $ v_i $ and $ v_j $. We investigate the spectral properties of this matrix,…
We obtain new partial results supporting the spectral set conjecture in dimension 1.
The reciprocal Pascal matrix has entries $\binom{i+j}{j}^{-1}$. Explicit formullae for its LU-decomposition, the LU-decomposition of its inverse, and some related matrices are obtained. For all results, $q$-analogues are also presented.
In this work, we study the spectral properties of matrix Hamiltonians generated by linearizing the nonlinear Schr\"odinger equation about soliton solutions. By a numerically assisted proof, we show that there are no embedded eigenvalues for…
We present a prescription for forming matrices with specified eigenvalues and known eigenvectors. With this method, we can form Hermitian, anti-Hermitian, symmetric and general matrices with arbitrary eigenvalues. In addition we propose an…
One matrix structure in the area of monotone Boolean functions is defined here. Some of its combinatorial, algebraic and algorithmic properties are derived. On the base of these properties, three algorithms are built. First of them…
In this paper we study the structure and give bounds for the eigenvalues of the $n\times n$ matrix, which $ij$ entry is $(i,j)^\alpha[i,j]^\beta$, where $\alpha,\beta\in\Rset$, $(i,j)$ is the greatest common divisor of $i$ and $j$ and…
This paper investigates spectral properties of certain classes of positive operators originated from different matrices appeared in linear complementarity problem. These positive operators play a crucial role in various areas of mathematics…
In these notes we review recent progress (and, in Section \ref{sec:ados}, we announce a new result) concerning the statistical properties of the spectrum of Wigner random matrices.
Motivated by the conjectures formulated in 2003 by Tun\c{c}el et al., we study interlacing properties of the eigenvalues of $A\otimes B + B\otimes A$ for pairs of $n$-by-$n$ matrices $A, B$. We prove that for every pair of symmetric…
Lehmer constructs four classes of matrices constructed from roots of unity for which the characteristic polynomials and the $k$-th powers can be determined explicitly. Here we study a class of matrices which arise naturally in…
Motivated by studies of oscillator networks, we study the spectrum of the join of several normal matrices with constant row sums. We apply our results to compute the characteristic polynomial of the join of several regular graphs. We then…
This paper solves the following problem about Hermitian matrices related to the theory of $2$-structures:\emph{ }Let $n$ be a positive integer and $k$ be an integer with $k\in \{3,\ldots,n-3\}$. Characterize the Hermitian matrices $A$ such…
Consider the Jacobi operators $\cJ$ given by $(\cJ y)_n=a_ny_{n+1}+b_ny_n+a_{n-1}^*y_{n-1}$, $y_n\in \C^m$ (here $y_0=y_{p+1}=0$), where $b_n=b_n^*$ and $a_n:\det a_n\ne 0$ are the sequences of $m\ts m$ matrices, $n=1,..,p$. We study two…
Matrix functions extend scalar function concepts to linear operators, offering a unified framework with broad applications in mathematics, science, and engineering. Classical definitions--via power series, spectral calculus, or Jordan…
A large variety of dynamical processes that take place on networks can be expressed in terms of the spectral properties of some linear operator which reflects how the dynamical rules depend on the network topology. Often such spectral…
Spectral and numerical properties of classes of random orthogonal butterfly matrices, as introduced by Parker (1995), are discussed, including the uniformity of eigenvalue distributions. These matrices are important because the…
We describe extensive computational experiments on spectral properties of random objects - random cubic graphs, random planar triangulations, and Voronoi and Delaunay diagrams of random (uniformly distributed) point sets on the sphere). We…