We investigate interconnected aspects of hyperderivatives polynomials over finite fields, q -th powers polynomials, and specializations Vandermonde matrices. construct formulas for Carlitz multiplication coefficients using symmetric we prove identities hyperderivative power sums in terms the inverse matrix. As an application these results give a new proof theorem Thakur on explicit Anderson's s...

A MIMO radar system is conveniently modeled via random matrices, and its optimal design strongly relies on spectral properties of the matrix exploited to build the model itself. We offer a way to model a High Resolution Radar (HRR) detection in the MIMO case, based on recent results on the asymptotic spectral analysis of random Vandermonde matrices with entries lying on the unit circle. Achieva...

This paper is concerned with general analysis on the rank and row-redundancy of an array of circulants whose null space defines a QC-LDPC code. Based on the Fourier transform and the properties of conjugacy classes and Hadamard products of matrices, we derive tight upper bounds on rank and row-redundancy for general array of circulants, which make it possible to consider row-redundancy in const...

We consider the partition function for a matrix model with a global unitary invariant energy function. We show that the averages over the partition function of global unitary invariant trace polynomials of the matrix variables are the same when calculated with any choice of a global unitary fixing, while averages of such polynomials without a trace define matrixvalued correlation functions, tha...

The problem of polynomial regression in which the usual monomial basis is replaced by the Bernstein basis is considered. The coefficient matrix A of the overdetermined system to be solved in the least squares sense is then a rectangular Bernstein-Vandermonde matrix. In order to use the method based on the QR decomposition of A, the first stage consists of computing the bidiagonal decomposition ...

We address the problem of tensor decomposition in application to direction-of-arrival (DOA) estimation for two-dimensional transmit beamspace (TB) multiple-input multiple-output (MIMO) radar. A general higher-order model that enables computationally efficient DOA is designed. Whereas other decomposition-based methods treat all factor matrices as arbitrary, essence proposed method fully exploit ...

Given a set T ⊆ GF(q), |T | = t, wT is defined as the smallest positive integer k for which ∑ y∈T y k 6= 0. It can be shown that wT ≤ t always and wT ≤ t − 1 if the characteristic p divides t. T is called a Vandermonde set if wT ≥ t−1 and a super-Vandermonde set if wT = t. This (extremal) algebraic property is interesting for its own right, but the original motivation comes from finite geometri...

We present new O(n3) algorithms that compute eigenvalues and eigenvectors to high relative accuracy in floating point arithmetic for the following types of matrices: symmetric Cauchy, symmetric diagonally scaled Cauchy, symmetric Vandermonde, and symmetric totally nonnegative matrices when they are given as products of nonnegative bidiagonal factors. The algorithms are divided into two stages: ...

Structured linear algebra techniques enable one to deal at once with various types of matrices, with features such as Toeplitz-, Hankel-, Vandermondeor Cauchy-likeness. Following Kailath, Kung and Morf (1979), the usual way of measuring to what extent a matrix possesses one such structure is through its displacement rank, that is, the rank of its image through a suitable displacement operator. ...