Zobrazeno 1 - 10
of 3 640
pro vyhledávání: '"15a18"'
Autor:
Guo, Krystal, Schmeits, Vincent
In this paper, we consider state transfer in quantum walks by using combinatorial methods. We generalize perfect state transfer in two-reflection discrete-time quantum walks to a notion that we call peak state transfer; we define peak state transfer
Externí odkaz:
http://arxiv.org/abs/2411.05560
For a given graph $G$, we aim to determine the possible realizable spectra for a generalized (or sometimes referred to as a weighted) Laplacian matrix associated with $G$. This specialized inverse eigenvalue problem is considered for certain families
Externí odkaz:
http://arxiv.org/abs/2411.00292
We study the minimum number of distinct eigenvalues over a collection of matrices associated with a graph. Lower bounds are derived based on the existence or non-existence of certain cycle(s) in a graph. A key result proves that every Johnson graph h
Externí odkaz:
http://arxiv.org/abs/2411.00250
Autor:
Fan, Yi-Zheng
Hu and Ye conjectured that for a $k$-th order and $n$-dimensional tensor $\mathcal{A}$ with an eigenvalue $\lambda$ and the corresponding eigenvariety $\mathcal{V}_\lambda(\mathcal{A})$, $$\mathrm{am}(\lambda) \ge \sum_{i=1}^\kappa \mathrm{dim}(V_i)(
Externí odkaz:
http://arxiv.org/abs/2410.20830
A real matrix $Q$ is quasi-orthogonal if $Q^{\top}Q=qI$, for some positive real number $q$. We prove that any $n\times n$ skew-symmetric matrix $S$ is a principal sub-matrix of a skew-symmetric quasi-orthogonal matrix $Q$, called a quasi-orthogonal e
Externí odkaz:
http://arxiv.org/abs/2410.19594
Autor:
Nayak, Soumyashant, Shekhawat, Renu
For $A \in M_m(\mathbb{C})$, Yamamoto's generalization of the spectral radius formula (1967) asserts that $\lim_{n \to \infty} s_j(A^n)^{\frac{1}{n}}$ is equal to the $j^{\textrm{th}}$-largest eigenvalue-modulus of $A$, where $s_j (A^n)$ denotes the
Externí odkaz:
http://arxiv.org/abs/2410.16318
Autor:
Lin, Jephian C. -H., Shirazi, Mahsa N
Given a graph and one of its weighted Laplacian matrix, a Fiedler vector is an eigenvector with respect to the second smallest eigenvalue. The Fiedler vectors have been used widely for graph partitioning, graph drawing, spectral clustering, and findi
Externí odkaz:
http://arxiv.org/abs/2410.09736
Autor:
Pazzis, Clément de Seguins
Let F be a field. We investigate the greatest possible dimension t_n(F) for a vector space of n-by-n matrices with entries in F and in which every element is triangularizable over the ground field F. It is obvious that t_n(F) is greater than or equal
Externí odkaz:
http://arxiv.org/abs/2410.07942
We say that a semigroup of matrices has a submultiplicative spectrum if the spectrum of the product of any two elements of the semigroup is contained in the product of the two spectra in question (as sets). In this note we explore an approximate vers
Externí odkaz:
http://arxiv.org/abs/2410.02617
Autor:
Kumari, Komal, Panigrahi, Pratima
Very recently Ma and Wu \cite{wu2024generalization} obtained a generalization of Fielder's lemma and applied to find adjacency, Laplacian, and signless Laplacian spectra of $P_n-$ product of commuting graphs. In this paper, we give a generalization o
Externí odkaz:
http://arxiv.org/abs/2409.20105