Related papers: Inertia laws and localization of real eigenvalues …
We describe the connection between inversion symmetry breaking and criticality in free fermionic lattice models. It is shown that for translation-invariant spinless fermions, the breaking of this symmetry in the ground state implies…
Standard perturbation theory of eigenvalue problems consists of obtaining approximations of eigenmodes in the neighborhood of an operator where the corresponding eigenmode is known. Nevertheless, if the corresponding eigenmodes of several…
This paper investigates the necessary and sufficient algebraic conditions to a constrained system of Sylvester-type quaternion tensor equations. An explicit formula of the general solution regarding the Moore-Penrose inverses of some block…
The main scope of this article is to define the concept of principal eigenvalue for fully non linear second order operators in bounded domains that are elliptic and homogenous. In particular we prove maximum and comparison principle, Holder…
This paper offers a review of numerical methods for computation of the eigenvalues of Hermitian matrices and the singular values of general and some classes of structured matrices. The focus is on the main principles behind the methods that…
The celebrated elliptic law describes the distribution of eigenvalues of random matrices with correlations between off-diagonal pairs of elements, having applications to a wide range of physical and biological systems. Here, we investigate…
Scale invariance in the theory of classical mechanics can be induced from the scale invariance of background fields. In this paper we consider the relation between the scale invariance and the constants of particle motion in a self-similar…
When an eigenvector of a semi-bounded operator is positive, we show that a remarkably simple argument allows to obtain upper and lower bounds for its associated eigenvalue. This theorem is a substantial generalization of Barta-like…
The entropic formulation of the inertia and the gravity relies on quantum, geometrical and informational arguments. The fact that the results are completly classical is missleading. In this paper we argue that the entropic formulation…
This work investigates the validity of the generalized second law of thermodynamics in modified f(R) Horava-Lifshitz gravity proposed by Chaichian et al (2010) [Class. Quantum Grav. 27 (2010) 185021], which is invariant under…
For complex Wigner-type matrices, i.e. Hermitian random matrices with independent, not necessarily identically distributed entries above the diagonal, we show that at any cusp singularity of the limiting eigenvalue distribution the local…
We investigate the eigenvalues statistics of ensembles of normal random matrices when their order N tends to infinite. In the model the eigenvalues have uniform density within a region determined by a simple analytic polynomial curve. We…
Two inverse-free iterative methods are developed for solving Sylvester matrix equations when the spectra of the coefficient matrices are on, or near, known disjoint subintervals of the real axis. Both methods use the recently-introduced…
Intrinsic wavelet transforms and wavelet estimation methods are introduced for curves in the non-Euclidean space of Hermitian positive definite matrices, with in mind the application to Fourier spectral estimation of multivariate stationary…
We consider $N\times N$ Hermitian random matrices with i.i.d. entries. The matrix is normalized so that the average spacing between consecutive eigenvalues is of order $1/N$. We study the connection between eigenvalue statistics on…
Eigenvalue and eigenpair backward errors are computed for matrix pencils arising in optimal control. In particular, formulas for backward errors are developed that are obtained under block-structure-preserving and…
Let $\beta>0$ and consider an $n$-point process $\lambda_1, \lambda_2,..., \lambda_n$ from Hermite $\beta$ ensemble on the real line $\mathbb{R}$. Dumitriu and Edelman discovered a tri-diagonal matrix model and established the global Wigner…
It was generally believed that, in general relativity, the fundamental laws of nature should be invariant or covariant under a general coordinate transformation. In general relativity, the equivalence principle tells us the existence of a…
Eigenvalues inequalities involving (log) convex/concav functions and Hermitian matrices, positive unital maps are considered. Simple proofs of Bhatia-Kittaneh inequality and Naimark dilation theorem are given.
We propose a general framework to study the stability of the subspace spanned by $P$ consecutive eigenvectors of a generic symmetric matrix ${\bf H}_0$, when a small perturbation is added. This problem is relevant in various contexts,…