Related papers: Observer Design over Hypercomplex Quaternions
We investigate the problem of determining the zeros of quaternionic polynomials using matrix method. In a recent paper, Dar et al. \cite{RD} proved that the zeros of a quaternionic polynomial and the left eigenvalues of the corresponding…
It is natural to study octonion Hilbert spaces as the recently swift development of the theory of quaternion Hilbert spaces. In order to do this, it is important to study first its algebraic structure, namely, octonion modules. In this…
This letter investigates the design of a class of infinite-dimensional observers for one dimensional (1D) boundary controlled port-Hamiltonian systems (BC-PHS) defined by differential operators of order $N \geq 1$. The convergence of the…
We introduce the concept of Almost-Companion Matrix (ACM) by relaxing the non-derogatory property of the standard Companion Matrix (CM). That is, we define an ACM as a matrix whose characteristic polynomial coincides with a given monic and…
It is known that the quaternion algebras are central simple algebras and also clifford algebras. In this paper, we introduce a new class of quaternions called Lucas-Leonardo p-quaternions and derive several fundamental properties of these…
We give examples of quaternion and octonion division algebras over a field $F$ of characteristic $2$ that split over a purely inseparable extension $E$ of $F$ of degree $\geq 4$ but that do not split over any subextension of $F$ inside $E$…
Due to the noncommutative nature of quaternions and octonions we introduce barred operators. This objects give the opportunity to manipulate appropriately the hypercomplex fields. The standard problems arising in the definitions of…
Let $L$ be a separable quadratic extension of either $\mathbb{Q}$ or $\mathbb{F}_q(t)$. We propose efficient algorithms for finding isomorphisms between quaternion algebras over $L$. Our techniques are based on computing maximal one-sided…
Recently, in weighted automata theory the weight structure of strong bimonoids has found much interest; they form a generalization of semirings and are closely related to near-semirings studied in algebra. Here, we define polynomials over a…
We extend the close interplay between continued fractions, orthogonal polynomials, and Gaussian quadrature rules to several variables in a special but natural setting which we characterize in terms of moment sequences. The crucial condition…
The main properties of hypercomplex generalization of quaternion system as antiquaternion are presented in this article. Definitions and studied of antiquaternions conjugation are introduced, their norm and zero divisor, and how to perform…
Numerous attempts have been made to replicate the success of complex-valued algebra in engineering and science to other hypercomplex domains such as quaternions, tessarines, biquaternions, and octonions. Perhaps, none have matched the…
We provide sufficient conditions for systems of polynomial equations over general (real or complex) algebras to have a solution. This generalizes known results on quaternions, octonions and matrix algebras. We also generalize the…
Explicit expressions are given for the actions and radial matrix elements of basic radial observables on multi-dimensional spaces in a continuous sequence of orthonormal bases for unitary SU(1,1) irreps. Explicit expressions are also given…
Quaternion analysis is considered in full details where a new analyticity condition in complete analogy to complex analysis is found. The extension to octonions is also worked out.
Within the framework of exterior algebra, the concept of time-like quaternions has been previously established. This paper advances beyond the existing structure by elucidating the procedure for constructing time-like quaternions with the…
High dimensional expanders simultaneously satisfying spectral and combinatorial (coboundary) expansion have recently played a major role in breakthroughs in PCP and coding theory, but the only known construction of such complexes is…
We construct explicit complex-valued $p$-harmonic functions and harmonic morphisms on the classical compact symmetric complex and quaternionic Grassmannians. The ingredients for our construction method are joint eigenfunctions of the…
The study of good nonregular fractional factorial designs has received significant attention over the last two decades. Recent research indicates that designs constructed from quaternary codes (QC) are very promising in this regard. The…
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…