14,622 Results Found

In this paper, we use semi-tensor product of quaternion matrices, $\mathcal{L}$-representation of quaternion matrices, and $\mathbf{GH}$-representation of special quaternion matrices such as quaternion (anti)-centrosymmetric matrices to solve the special solutions of quate...

In this paper, we consider certain special sine, tangent, and cotangent symmetric matrices, along with their associated integer matrices. We present interesting relationships that connect these matrices. Relevant examples of the corresponding matrice...

Dual algebra plays an important role in kinematic synthesis and dynamic analysis, but there are still few studies on dual quaternion matrix theory. This paper provides an efficient method for solving the QLY least squares problem of the dual quaterni...

A trivially zero minor of a matrix is a minor having all its terms in the Leibniz formula equal to zero. A matrix is superregular if all of its minors that are not trivially zero are nonzero. In the area of Coding Theory, superregular matrices over f...

Extensions of Filbert and Lilbert matrices are addressed in this work. They are reciprocal Hankel matrices based on Fibonacci and Lucas numbers, respectively, and both are related to Hilbert matrices. The Neville elimination is applied to provide exp...

We introduce a family of models, which we name matrix models associated with children’s drawings—the so-called dessin d’enfant. Dessins d’enfant are graphs of a special kind drawn on a closed connected orientable surface (in the sky). The vertices of...

In this study, we have established the bounds for the \(\ell_p \) norms and the Euclidean norm of almost GCD Cauchy-Toeplitz, almost GCD Cauchy-Hankel and GCD matrices, respectively.

Given a real symmetric matrix, several inclusion and exclusion intervals containing its eigenvalues can be given. In this paper, for symmetric positive Toeplitz matrices, we provide an inclusion interval and, under an additional hypothesis, we also g...

The elements of the bidiagonal decomposition (BD) of a totally positive (TP) collocation matrix can be expressed in terms of symmetric functions of the nodes. Making use of this result, and studying the relation between Wronskian and collocation matr...

For positive Hankel matrices, an interval containing all eigenvalues is obtained. With a stronger condition, we also construct two sharper intervals for the eigenvalue localization. The total positivity of positive Hankel matrices is analyzed. The re...

Starting from the very first principles we derive explicit parameterizations of the ortho-symplectic matrices in the real four-dimensional Euclidean space. These matrices depend on a set of four real parameters which splits naturally as a union of th...

Max–min algebra (called also fuzzy algebra) is an extremal algebra with operations maximum and minimum. In this paper, we study the robustness of Monge matrices with inexact data over max–min algebra. A matrix with inexact data (also call...

The behavior of the spectra of symmetric block-type random matrices with symmetric blocks of high dimensionality is considered in this paper. Under minimal conditions regarding the distributions of matrix block elements (Lindeberg conditions), the un...

Min and max matrices are structured matrices that appear in diverse mathematical and computational applications. Their inherent structures facilitate highly accurate numerical solutions to algebraic problems. In this research, the total positivity of...

The class of H-matrices, also known as Generalized Diagonally Dominant (GDD) matrices, plays an important role in many areas of applied linear algebra, as well as in a wide range of applications, such as in dynamical analysis of complex networks that...

Firstly, the relationships among strictly diagonally dominant ( $SDD$ ) matrices, doubly strictly diagonally dominant ( $DSDD$ ) matrices, eventually $SDD$ matrices and eventually $DSDD$ matrices are considered. Secondly...

Index matrices are an extension of the ordinary matrices with explicitly assigned index sets on both their rows and columns, forming an advanced mathematical structure used for specialized data modeling and problem-solving. In the present paper, a ne...

Star-convexity of the eigenvalue region for the set of $n\times n$ stochastic matrices has already been proven, for $n\ge 2$, by Dmitriev and Dynkin. The star-convexity property enables full determination of the eigenvalue region by its boundary. This st...

We investigate the properties of matrices that emerge from the application of Fourier series to Jacobi matrices. Specifically, we focus on functions defined by the coefficients of a Fourier series expressed in orthogonal polynomials. In the operation...

The relationship among eigenvalues, singular values, and quadratic forms associated with linear transforms of doubly stochastic matrices has remained an important topic since 1949. The main objective of this article is to present some useful theorems...

In this work, an analogue to the Pauli spin matrices is presented and investigated. The proposed Hermitian spin matrices exhibit four symmetries for spin-1/n particles. The spin projection operators are derived, and the electrodynamics for hypothetic...

In this paper, we study the properties of faces and exposed faces of the cone of copositive matrices (copositive cone), paying special attention to issues related to their geometric structure. Based on the concepts of zero and minimal zero vectors, w...

In simulating Quantum Computing by using the circuit model the size of the matrices to deal with, together with the number of products and additions required to apply every quantum gate becomes a really hard computational restriction. This paper pres...

The paper is a survey of the recent results of the author on the perturbations of matrices. A part of the results presented in the paper is new. In particular, we suggest a bound for the difference of the determinants of two matrices which refines th...

We address the inverse extremal eigenvalue problem (IEEP) for multi-arrowhead pentadiagonal matrices, a structured class that combines pentadiagonal bandwidth with an alternating arrowhead structure. We identify four distinct structural classes based...

Figural matrices tasks are one of the most prominent item formats used in intelligence tests, and their relevance for the assessment of cognitive abilities is unquestionable. However, despite endeavors of the open science movement to make scientific...

In this paper, we address the extremal inverse eigenvalue problem for pentadiagonal matrices. We provide sufficient conditions for their existence and realizability through new constructions that consider spectral data of its leading principal submat...

Block matrices play an important role in all branches of pure and applied mathematics. In this paper, we study the two fundamental concepts: inverses and determinants of general $n\times n$ block matrices. In the first part, the inverses of $2\times 2$ b...

There are two sets of four-by-four matrices introduced by Dirac. The first set consists of fifteen Majorana matrices derivable from his four γ matrices. These fifteen matrices can also serve as the generators of the group SL(4, r). The second set con...

This article considers arrowhead and diagonal-plus-rank-one matrices in ${\mathbb{F}}^{n\times n}$ where $\mathbb{F}\in \{\mathbb{R},\mathbb{C},\mathbb{H}\}$ and where $\mathbb{H}$ is a noncommutative algebra of quaternions. We provide unified formulas for fast determinants and inverses for considered matrices. Th...

The eigenvalue bounds of interval matrices are often required in some mechanical and engineering fields. In this paper, we improve the theoretical results presented in a previous paper “A property of eigenvalue bounds for a class of symmetric t...

Asymmetric interaction matrices encode the linear coupling structure and directed interaction patterns that arise in mathematical models of complex networks across ecology, finance, and machine learning, yet their geometric structure as points on a s...

This paper aims to simplify the form of the MPBT inverse, further explore its properties, and discuss when it coincides with other generalized inverses. Notably, the MPBT inverse coincides with the Moore–Penrose inverse when the index of the ma...

The structure of the random matrices introduced in this work is given by deterministic matrices—the skeletons of the random matrices—built with an algorithm of matrix substitutions with entries in a finite field of integers modulo some pr...

Circulant matrices have attracted interest due to their rich algebraic structures and various applications. In this paper, the concept of vector-circulant matrices over finite fields is studied as a generalization of circulant matrices. The algebraic...

Fisher matrices play an important role in experimental design and in data analysis. Their primary role is to make predictions for the inference of model parameters—both their errors and covariances. In this short review, I outline a number of extensi...

The nonnegative inverse eigenvalue problem (NIEP) consists of finding necessary and sufficient conditions for the existence of a nonnegative matrix with a given list of complex numbers as its spectrum. If the matrix is required to be Leslie (doubly L...

We proved the local Marchenko–Pastur law for sparse sample covariance matrices that corresponded to rectangular observation matrices of order $n\times m$ with $n/m\to y$ (where $y>0$) and sparse probability $n{p}_n>{log}^{\beta }n$ (where $\beta >0$)....

A fundamental objective in the study of convex cones is the description and analysis of their extreme rays. In the case of the copositive cone, these rays are generated by extremal copositive matrices, which encode the boundary structure of the cone...

This work aims to study the interplay between the Wilson–Cowan model and connection matrices. These matrices describe cortical neural wiring, while Wilson–Cowan equations provide a dynamical description of neural interaction. We formulate...

The numerical approximation of both eigenvalues and singular values corresponding to a class of totally positive Bernstein–Vandermonde matrices, Bernstein–Bezoutian structured matrices, Cauchy—polynomial-Vandermonde structured matri...

This paper investigates the spectral properties of block circulant matrices with high-order symmetric (or Hermitian) blocks. We analyze cases with dependent or sparse independent entries within these blocks. Additionally, we analyze the distribution...

The measure of sphericity for positive semi-definite matrices plays a crucial role in understanding their geometric properties, especially in high-dimensional settings. This paper introduces a robust measure of sphericity, which remains invariant und...

The rapid and accurate transfer of information is essential in today’s digital world, where error detecting and correcting codes play a crucial role. In this context, Fibonacci numbers have been extensively applied in coding theory, particularl...

Dilation matrices are important in multiple subdivision and multiple multiresolution analysis, as they govern the process of data refinement and play a crucial role in capturing directional features. One common limitation in the existing methods is t...

In this paper, an upper bound on the spectral radius $\rho (A\circ B)$ for the Hadamard product of two nonnegative matrices (A and B) and the minimum eigenvalue $\tau (C★D)$ of the Fan product of two M-matrices (C and D) are research...

The distribution of eigenvalues and the upper bounds for the spread of interval matrices are significant in various fields of mathematics and applied sciences, including linear algebra, numerical analysis, control theory, and combinatorial optimizati...

Honey, honey extracts, and bee products belong to traditionally used bioactive molecules in many areas. The aim of the study was primarily to evaluate the effect of cosmetic matrices containing honey and bee products on the skin. The study is complem...

A set to locate all eigenvalues for matrices with a constant main diagonal entry is given, and it is proved that this set is tighter than the well-known Geršgorin set, the Brauer set and the set proposed in (Linear and Multilinear Algebra, 60:...

The spectrum of a matrix contains information essential for understanding the dynamics of the real system behind the matrix. Knowledge of eigenvalues and generalized eigenvalues is of great importance in stability analysis. In this paper, we present...