Related papers: Block Diagonalization of Quaternion Circulant Matr…
A discrete Fourier analysis on the dodecahedron is studied, from which results on a tetrahedron is deduced by invariance. The results include Fourier analysis in trigonometric functions, interpolation and cubature formulas on these domains.…
This work provides a quaternioinc reprsentation for real symplectic matrices in dimension four, analogous to the pair of unit quaternions representation for special orthogonal matrices. In the process of finding formulae for this…
We consider a new splitting based on the Sherman-Morrison-Woodbury formula, which is particularly effective with iterative methods for the numerical solution of large linear systems. These systems involve matrices that are perturbations of…
Dual quaternions and dual quaternion matrices have garnered widespread applications in robotic research, and its spectral theory has been extensively studied in recent years. This paper introduces the novel concept of the dual complex…
The purpose of this paper is to derive the Hoffman-Wielandt inequality and its generalization for quaternion matrices. Diagonalizability of the block companion matrix of certain quadratic (linear) quaternion matrix polynomials is brought…
Over the past century, a correlation has been an essential mathematical technique utilized in engineering sciences, including practically every signal/image processing field. This paper describes an effective method of calculating the…
The explicit computation of higher-point conformal blocks in any dimension is usually a challenging task. For two-dimensional conformal field theories in Euclidean signature, the oscillator formalism proves to be very efficient. We…
This paper establishes new upper bounds for the right eigenvalues of monic matrix polynomials over the quaternion division algebra. The noncommutative nature of quaternion multiplication presents fundamental challenges in eigenvalue…
The renewed interest in investigating quaternionic quantum mechanics, in particular tunneling effects, and the recent results on quaternionic differential operators motivate the study of resolution methods for quaternionic differential…
In structure from motion, quadrifocal tensors capture more information than their pairwise counterparts (essential matrices), yet they have often been thought of as impractical and only of theoretical interest. In this work, we challenge…
Topological phase classifications have been intensively studied via machine-learning techniques where different forms of the training data are proposed in order to maximize the information extracted from the systems of interests. Due to the…
In this work, a quaternion-valued model is proposed in lieu of the Clarke's \alpha, \beta transformation to convert three-phase quantities to a hypercomplex single-phase signal. The concatenated signal can be used for harmonic distortion…
Quaternion-valued differential equations (QDEs) is a new kind of differential equations which have many applications in physics and life sciences. The largest difference between QDEs and ODEs is the algebraic structure. On the…
Delaunay triangulations of a point set in the Euclidean plane are ubiquitous in a number of computational sciences, including computational geometry. Delaunay triangulations are not well defined as soon as 4 or more points are concyclic but…
A hermitian matrix can be parametrized by a set consisting of its determinant and the eigenvalues of its submatrices. We established a group of equations which connect these variables with the mixing parameters of diagonalization. These…
Bilinear feature transformation has shown the state-of-the-art performance in learning fine-grained image representations. However, the computational cost to learn pairwise interactions between deep feature channels is prohibitively…
In this article, specific definitions of the Moore-Penrose inverse, Drazin inverse of the quaternion tensor and the inverse along two quaternion tensors are introduced under the T-product. Some characterizations, representations and…
In this paper, we give several matrix representations for the Horadam quaternions. We derive several identities related to these quaternions by using the matrix method. Since quaternion multiplication is not commutative, some of our results…
Quaternion optimization has attracted significant interest due to its broad applications, including color face recognition, video compression, and signal processing. Despite the growing literature on quadratic and matrix quaternion…
The matrix functions can be defined by Cauchy's integral formula and can be approximated by the linear combination of inverses of shifted matrices using a quadrature formula. In this paper, we show a concrete construction of a framework to…