We study random normal matrix models whose eigenvalues tend to be distributed within a narrow “band” around the unit circle of width proportional 1∕n, where n is size matrices. For general radially symmetric potentials with various boundary conditions, we derive scaling limits correlation functions, some which appear in previous literature notably context almost-Hermitian also obtain that fluct...

The Hermitian Lanczos method for Hermitian matrices has a wellknown connection with a 3-term recurrence for polynomials orthogonal on a discrete subset of R. This connection disappears for normal matrices with the Arnoldi method. In this paper we consider an iterative method that is more faithful to the normality than the Arnoldi iteration. The approach is based on enlarging the set of polynomi...

This paper presents techniques for digital image watermarking based on eigenvalue decomposition of normal matrices. The introduced methods are convenient and self-explanatory, achieve satisfactory results, as well as require less and easy computations compared to some current methods. Through the proposed methods, host images and watermarks are transformed to the space of normal matrices, and t...

An approach, based on the Smith Normal Form, is introduced to study the spectra of symmetric matrices with a given graph. The approach serves well to explain how the path cover number (resp. diameter of a tree T ) is related to the maximal multiplicity MaxMult(T ) occurring for an eigenvalue of a symmetric matrix whose graph is T (resp. the minimal number q(T ) of distinct eigenvalues over the ...

The rank subtractivity partial ordering is defined on Cn×n (n ≥ 2) by A ≤− B⇔ rank(B−A) = rankB− rankA, and the star partial ordering by A ≤∗ B⇔ A∗A = A∗B ∧ AA∗ = BA∗. If A and B are normal, we characterize A ≤− B. We also show that then A ≤− B ∧ AB = BA⇔ A ≤∗ B⇔ A ≤− B ∧ A ≤− B. Finally, we remark that some of our results follow from well-known results on EP matrices.