Related papers: Spectral symmetry in conference matrices
The eccentricity matrix of a connected graph $G$ is obtained from the distance matrix of $G$ by retaining the largest distances in each row and each column, and setting the remaining entries as $0$. In this article, a conjecture about the…
In [Rank-Width and Well-Quasi-Ordering of Skew-Symmetric or Symmetric Matrices, arXiv:1007.3807v1] Oum proved that, for a fixed finite field $\mathbf{F}$, any infinite sequence $M_1,M_2,...$ of (skew) symmetric matrices over $\mathbf{F}$ of…
In this paper Seidel matrices are studied, and their spectrum and several related algebraic properties are determined for order $n\leq 13$. Based on this Seidel matrices with exactly three distinct eigenvalues of order $n\leq 23$ are…
The eccentricity matrix of a simple connected graph is obtained from the distance matrix by only keeping the largest distances for each row and each column, whereas the remaining entries become zero. This matrix is also called the…
In this article, following [A.~Daneshgar, M.~Hejrati, M.~Madani, {\it On cylindrical graph construction and its applications}, EJC, 23(1) p1.29, 45, 2016] we study the spectra of symmetric cylindrical constructs, generalizing some…
We consider spectra of $n$-by-$n$ irreducible tridiagonal matrices over a field and of their $n-1$-by-$n-1$ trailing principal submatrices. The real symmetric and complex Hermitian cases have been fully understood: it is necessary and…
A perfect matching in a graph $G$ is a set of nonadjacent edges covering every vertex of $G$. Motivated by recent progress on the relations between the eigenvalues and the matching number of a graph, in this paper, we aim to present a…
Matrices are the most common representations of graphs. They are also used for the representation of algebras and cluster algebras. This paper shows some properties of matrices in order to facilitate the understanding and locating…
This work provides a comprehensive theoretical framework for understanding the symmetry properties of High-Resolution NMR spectra. We analyze the conditions under which a spectrum exhibits mirror symmetry (palindromicity). We demonstrate…
We show that the spectral radius of an $N\times N$ random symmetric matrix with i.i.d. bounded centered but non-symmetrically distributed entries is bounded from above by $ 2 \*\sigma + o(N^{-6/11+\epsilon}), $ where $\sigma^2 $ is the…
Let $\mathbf{a}_{ij}$, $1\leq i\leq j\leq n$, be independent random variables and $\mathbf{a}_{ji}=\mathbf{a}_{ij}$, for all $i,j$. Suppose that every $\mathbf{a}_{ij}$ is bounded, has zero mean, and its variance is given by…
We study the equivalence between bipartiteness and symmetry of spectra of mixed graphs, for $\theta$-Hermitian adjacency matrices defined by an angle $\theta \in (0, \pi]$. We show that this equivalence holds when, for example, an angle…
We investigate the properties of positive definite and positive semi-definite symmetric matrices within the framework of symmetrized tropical algebra, an extension of tropical algebra adapted to ordered valued fields. We focus on the…
We consider real orthogonal $n\times n$ matrices whose diagonal entries are zero and off-diagonal entries nonzero, which we refer to as $\mathrm{OMZD}(n)$. We show that there exists an $\mathrm{OMZD}(n)$ if and only if $n\neq 1,\ 3$, and…
In this paper, spectral properties of matrices with (complex) zeon entries are investigated. It is shown that when $A$ is an $m\times m$ self-adjoint matrix whose characteristic polynomial $\chi_A(u)$ has $m$ ``spectrally simple'' zeros…
We investigate connections between the symmetries (automorphisms) of a graph and its spectral properties. Whenever a graph has a symmetry, i.e. a nontrivial automorphism $\phi$, it is possible to use $\phi$ to decompose any matrix…
We introduce a hypergraph matrix, named the unified matrix, and use it to represent the hypergraph as a graph. We show that the unified matrix of a hypergraph is identical to the adjacency matrix of the associated graph. This enables us to…
We study n by n symmetric random matrices H, possibly discrete, with iid above-diagonal entries. We show that H is singular with probability at most exp(-n^c), and the spectral norm of the inverse of H is O(sqrt{n}). Furthermore, the…
An alternating sign matrix is a square matrix satisfying (i) all entries are equal to 1, -1 or 0; (ii) every row and column has sum 1; (iii) in every row and column the non-zero entries alternate in sign. The 8-element group of symmetries…
Let $F_n$ be an $n$ by $n$ symmetric matrix whose entries are bounded by $n^{\gamma}$ for some $\gamma>0$. Consider a randomly perturbed matrix $M_n=F_n+X_n$, where $X_n$ is a random symmetric matrix whose upper diagonal entries $x_{ij}$…