Related papers: (K,L)-eigenvectors in max-min algebra

We analyze the expectation value of observables in a scalar theory on the fuzzy two sphere, represented as a generalized hermitian matrix model. We calculate explicitly the form of the expectation values in the large-N limit and demonstrate…

In this article we introduce a new method, which we call a mutation-sunflower method, for calculating max-eigenvectors of a nonnegative irreducible $n\times n$ matrix $A$. Our method works in the general irreducible case, but it is in…

Multidimensional minimax single facility location problems with Chebyshev distance are examined within the framework of idempotent algebra. A new algebraic solution based on an extremal property of the eigenvalues of irreducible matrices is…

The role of the normalized modularity matrix in finding homogeneous cuts will be presented. We also discuss the testability of the structural eigenvalues and that of the subspace spanned by the corresponding eigenvectors of this matrix. In…

We consider the eigenvalue problem $K x = \lambda x$. Our analysis focuses on the convergence rates of eigenvalue and spectral subspace approximations for compact linear integral operator $K$ with Green's kernels. By employing orthogonal…

We study an eigenvalue problem for the Laplacian on a compact K\"{a}hler manifold. Considering the $k$-th eigenvalue $\lambda_{k}$ as a functional on the space of K\"{a}hler metrics with fixed volume on a compact complex manifold, we…

For a large class of integrable quantum field theories we show that the S-matrix determines a space of fields which decomposes into subspaces labeled, besides the charge and spin indices, by an integer k. For scalar fields k is non-negative…

We investigate regularity properties of minimizers for non-autonomous convex variational integrands $F(x, \mathrm{D} u)$ with linear growth, defined on bounded Lipschitz domains $\Omega \subset \mathbb{R}^n$. Assuming appropriate…

We study the angles between the eigenvectors of a random $n\times n$ complex matrix $M$ with density $\propto \mathrm{e}^{-n\operatorname{Tr}V(M^*M)}$ and $x\mapsto V(x^2)$ convex. We prove that for unit eigenvectors…

In this paper, we propose an unconstrained framework for eigenvalue problems in both discrete and continuous settings. We begin our discussion to solve a generalized eigenvalue problem $A{\bf x} = \lambda B{\bf x}$ with two $N\times N$ real…

We prove that each eigenvalue l(k) of the Kirchhoff Laplacian K of a graph or quiver is bounded above by d(k)+d(k-1) for all k in {1,...,n}. Here l(1),...,l(n) is a non-decreasing list of the eigenvalues of K and d(1),..,d(n) is a…

The elaboration of new quantization methods has recently developed the interest in the study of subalgebras of the Lie algebra of polynomial vector fields over a Euclidean space. In this framework, these subalgebras define maximal…

If $A$ is an $n \times n$ Hermitian matrix with eigenvalues $\lambda_1(A),\dots,\lambda_n(A)$ and $i,j = 1,\dots,n$, then the $j^{\mathrm{th}}$ component $v_{i,j}$ of a unit eigenvector $v_i$ associated to the eigenvalue $\lambda_i(A)$ is…

Given a compact manifold equipped with a volume element and a Riemannian metric, we formulate and study a dual pair of optimization problems: one concerning smooth maps from the manifold into the Hilbert space $l^2$ and the other concerning…

In this paper, we show an optimal volume growth for self-shrinkers, and estimate a lower bound of the first eigenvalue of $\mathcal{L}$ operator on self-shrinkers, inspired by the first eigenvalue conjecture on minimal hypersurfaces in the…

By using the methods of Cauchy-Binet type formula and adjugate matrix respectively, a wonderful equality relating to the elements of eigenvectors, the eigenvalues and the submatrix eigenvalues is proved in arXiv:1908.03795. In the note, we…

We extend to infinite dimensional separable Hilbert spaces the Schur convexity property of eigenvalues of a symmetric matrix with real entries. Our framework includes both the case of linear, selfadjoint, compact operators, and that of…

This paper is concerned with the maximisation of the k'th eigenvalue of the Laplacian amongst flat tori of unit volume in dimension d as k goes to infinity. We show that in any dimension maximisers exist for any given k, but that any…

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 is a short review of recent work on fuzzy spaces in their relation to the M(atrix) theory and the quantum Hall effect. We give an introduction to fuzzy spaces and how the limit of large matrices is obtained. The complex projective…