Related papers: Dual Complex Adjoint Matrix: Applications in Dual …
Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…
We represent low dimensional quantum mechanical Hamiltonians by moderately sized finite matrices that reproduce the lowest O(10) boundstate energies and wave functions to machine precision. The method extends also to Hamiltonians that are…
Chart-based visual acuity measurements are used by billions of people to diagnose and guide treatment of vision impairment. However, the ubiquitous eye exam has no mechanism for reasoning about uncertainty and as such, suffers from a…
In this paper properties of the determinant of a Hermitian matrix are investigated, and determinantal representations of the inverse of a Hermitian coquaternionic matrix are given. By their using, Cramer's rules for left and right systems…
The same complex matrix model calculates both tachyon scattering for the c=1 non-critical string at the self-dual radius and certain correlation functions of half-BPS operators in N=4 super-Yang-Mills. It is dual to another complex matrix…
This paper revisits the topic of rotation estimation through the lens of special unitary matrices. We begin by reformulating Wahba's problem using $SU(2)$ to derive multiple solutions that yield linear constraints on corresponding…
The recent development of calibration algorithms has been driven into two major directions: (1) an increasing accuracy of mathematical approaches and (2) an increasing flexibility in usage by reducing the dependency on calibration objects.…
This article considers the problem of designing adaption and optimisation techniques for training quantum learning machines. To this end, the division algebra of quaternions is used to derive an effective model for representing computation…
In this paper we explore the role of duality principles within the problem of rotation averaging, a fundamental task in a wide range of computer vision applications. In its conventional form, rotation averaging is stated as a minimization…
We discuss the relationship between quaternion algebras and quadratic forms with a focus on computational aspects. Our basic motivating problem is to determine if a given algebra of rank 4 over a commutative ring R embeds in the 2x2-matrix…
Quaternion matrices are employed successfully in many color image processing applications. In particular, a pure quaternion matrix can be used to represent red, green and blue channels of color images. A low-rank approximation for a pure…
We introduce the notion of the Lie derivative in the context of dual quaternions that represent rigid motions and twists. First we define the wrench in terms of dual quaternions. Then we show how the Lie derivative helps understand how…
Random matrix theory is a powerful way to describe universal correlations of eigenvalues of complex systems. It also may serve as a schematic model for disorder in quantum systems. In this review, we discuss both types of applications of…
We propose a novel quaternion product unit (QPU) to represent data on 3D rotation groups. The QPU leverages quaternion algebra and the law of 3D rotation group, representing 3D rotation data as quaternions and merging them via a weighted…
The paper presents a new framework for complex Support Vector Regression as well as Support Vector Machines for quaternary classification. The method exploits the notion of widely linear estimation to model the input-out relation for…
Dual Bernstein polynomials find many applications in approximation theory, computational mathematics, numerical analysis and computer-aided geometric design. In this context, one of the main problems is fast and accurate evaluation both of…
Products and sums of random matrices have seen a rapid development in the past decade due to various analytical techniques available. Two of these are the harmonic analysis approach and the concept of polynomial ensembles. Very recently, it…
We introduce a novel eigenvalue algorithm for near-diagonal matrices inspired by Rayleigh-Schr\"odinger perturbation theory and termed Iterative Perturbative Theory (IPT). Contrary to standard eigenvalue algorithms, which are either…
The attitude space has been parameterized in various ways for practical purposes. Different representations gain preferences over others based on their intuitive understanding, ease of implementation, formulaic simplicity, and physical as…
Before a car-following model can be applied in practice, it must first be validated against real data in a process known as calibration. This paper discusses the formulation of calibration as an optimization problem, and compares different…