Related papers: Circulant matrices: norm, powers, and positivity
By the Choi matrix criteria it is easy to determine if a specific linear matrix map is completely positive, but to establish whether a linear matrix map is positive is much less straightforward. In this paper we consider classes of linear…
The $p$-norm of $r$-matrices generalizes the $2$-norm of $2$-matrices. It is shown that if a nonnegative $r$-matrix is symmetric with respect to two indices $j$ and $k$, then the $p$-norm is attained for some set of vectors such that the…
We give a new proof of universality properties in the bulk of spectrum of the hermitian matrix models, assuming that the potential that determines the model is globally $C^{2}$ and locally $C^{3}$ function (see Theorem \ref{t:U.t1}). The…
An exchangeable random matrix is a random matrix with distribution invariant under any permutation of the entries. For such random matrices, we show, as the dimension tends to infinity, that the empirical spectral distribution tends to the…
We introduce a definition of the volume for a general rectangular matrix, which for square matrices is equivalent to the absolute value of the determinant. We generalize results for square maximum-volume submatrices to the case of…
In this note, we generalize biharmonic equation for rotationally symmetric maps ([4], [16], [10]) to equivariant maps between model spaces and use it to give a complete classification of rotationally symmetric conformal biharmonic maps from…
A beam of rotating dipolar particles (molecules or clusters) will broaden when passed through an electric or magnetic field gradient region. This broadening, which is a common experimental observable, can be expressed in terms of the…
We study the existence and construction of circulant matrices $C$ of order $n\geq2$ with diagonal entries $d\geq0$, off-diagonal entries $\pm1$ and mutually orthogonal rows. These matrices generalize circulant conference ($d=0$) and…
We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…
We introduce circulance, a scalar measure for classifying time series of dynamical systems. Circulance captures the extent of temporal regularity or irregularity that is encoded in the topology of a directed ordinal pattern transition…
The main result of the note describes certain optimal-score partitions, which can be interpreted as optimal resource allocations. This result is based on the fact that any nonnegative square matrix whose column sums are the same as the…
Handelman (J. Operator Theory, 1981) proved that if the spectral radius of a matrix $A$ is a simple root of the characteristic polynomial and is strictly greater than the modulus of any other root, then $A$ is conjugate to a matrix $Z$ some…
We investigate spectral conditions on Hermitian matrices of roots of unity. Our main results are conjecturally sharp upper bounds on the number of residue classes of the characteristic polynomial of such matrices modulo ideals generated by…
We characterize the infimum of a matrix norm of a square matrix A induced by an absolute norm, over the fields of real and complex numbers. Usually this infimum is greater than the spectral radius of A. If A is sign equivalent to a…
Motivated by Hirano-Tominaga's work \cite{HT} on rings for which every element is a sum of two idempotents and by de Seguins Pazzis's results \cite{de} on decomposing every matrix over a field of positive characteristic as a sum of…
We present a systematic study on the linear convergence rates of the powers of (real or complex) matrices. We derive a characterization when the optimal convergence rate is attained. This characterization is given in terms of…
This paper contains a re-evaluation of the spectral approach and factorizability for regular matrix polynomials. In addition, solvent theory is extended from the monic and comonic cases to the regular case. The classification of extended…
The cyclotomic matrix is commonly used to arrange cyclotomic numbers in a convenient format. A natural question is whether the structure of the matrix can reflect properties of these numbers. In this article, we examine cyclotomic numbers…
A form in a polynomial ring over a field is said to be homaloidal if its polar map is a Cremona map, i.e., if the rational map defined by the partial derivatives of the form has an inverse rational map. The object of this work is the search…
A classical theorem of Balcar, Pelant, and Simon says that there is a base matrix of height h, where h is the distributivity number of P(omega)/fin. We show that if the continuum c is regular, then there is a base matrix of height c, and…