Related papers: A Note On The Spectral Norms of The Matrices Conne…
Sum rules are elegant formulas that relate entropy functionals to coefficients associated with orthogonal polynomials [Sim11]. In a series of paper (see for example [GNR16], [GNR17], [BSZ18a], [BSZ18b]), interesting connections have been…
We study formal power series which can be interpreted as interpolations of Fibonacci and Lucas polynomials with even (or odd) indices.
In this article, we consider two proper double splittings satisfying certain conditions, of a semi-monotone rectangular matrix A and derive new comparison results for the spectral radii of the correspond ing iteration matrices. These…
The spectral norm of a Boolean function $f:\{0,1\}^n \to \{-1,1\}$ is the sum of the absolute values of its Fourier coefficients. This quantity provides useful upper and lower bounds on the complexity of a function in areas such as learning…
In this paper, we find the sums in closed form of certain type of Lucas-related convergent series. More precisely, we generalize the results already obtained by the author in his arXiv paper entitled: "Summation of certain infinite…
The joint spectral radius of a set of matrices is a measure of the maximal asymptotic growth rate that can be obtained by forming long products of matrices taken from the set. This quantity appears in a number of application contexts but is…
We study the spectral measure of large Euclidean random matrices. The entries of these matrices are determined by the relative position of $n$ random points in a compact set $\Omega_n$ of $\R^d$. Under various assumptions we establish the…
We evaluate various binomial sums involving the powers of Fibonacci and Lucas numbers.
We derive exact equations that determine the spectra of undirected and directed sparsely connected regular graphs containing loops of arbitrary length. The implications of our results to the structural and dynamical properties of networks…
This paper first discusses the size and orientation of hat supertiles. Fibonacci and Lucas sequences, as well as a third integer sequence linearly related to the Lucas sequence are involved. The result is then generalized to any aperiodic…
We consider an indexed class of real symmetric random matrices which generalize the symmetric Hankel and Reverse Circulant matrices. We show that the limiting spectral distributions of these matrices exist almost surely and the limit is…
We investigate various classes of metrics on the integers, which induce the F\"urstenberg topology and establish the connection between the metrics and the topology. We analyze the norm-like mappings underlying these metrics, with respect…
This note deals with the direct and inverse spectral analysis for a class of infinite band symmetric matrices. This class corresponds to operators arising from difference quations with usual and inner boundary conditions. We give a…
We use super-spectral curve to investigate irregular conformal states of integer and half-odd integer rank. The spectral curve is the loop equation of supersymmetrized irregular matrix model. The case of integer rank corresponds to the…
For an arbitrary homogeneous linear recurrence sequence of order d with constant coefficients, we derive recurrence relations for all subsequences with indices in arithmetic progression. The coefficients of these recurrences are given…
We study directions along which the norms of vectors are preserved under a linear map. In particular, we find families of matrices for which these directions are determined by integer vectors. We consider the two-dimensional case in detail,…
We give new identities for some symmetric polynomials. As applications of these identities, we obtain some formulas for a higher order analogue of Fibonacci and Lucas numbers.
In this text we study the regularity of matrices with special polynomial entries. Barring some mild conditions we show that these matrices are regular if a natural limit size is not exceeded. The proof draws connections to generalized…
The number of non-negative integer matrices with given row and column sums appears in a variety of problems in mathematics and statistics but no closed-form expression for it is known, so we rely on approximations of various kinds. Here we…
Inequalities for norms of different versions of the geometric mean of two positive definite matrices are presented.