By using the complex representation of quaternion matrices, the Moore–Penrose generalized inverse and the Kronecker product of matrices, the expressions of the least squares η-Hermitian solution with the least norm and the expressions of the least squares η-anti-Hermitian solution with the least norm are derived for the matrix equation AXB+CXD = E over quaternions.

Complex analyticity is generalized to hypercomplex functions, quaternion or octonion, in such a manner that it includes the standard complex definition and does not reduce analytic functions to a trivial class. A brief comparison with other definitions is presented. 1991 Mathematics Subject Classifications: 11R52, 30G35, 46S20.

~omplex analyticity is generalized to hypercomplex functions, quaternion or octonion, in such a manner that it’ includes the standard complex definition and does not reduce analytic functions to a trivial class. A brief comparison with other definitions is presented. @ 2003 Elsevier Ltd. All rights reserved. Keywords-&uaternions, Analytic functions, Differential operators.

A free bimodule resolution is constructed for the integral group ring of the dihedral group of order 4m. This resolution is applied for a description, in terms of generators and defining relations, of the Hochschild cohomology algebra of this group ring. Introduction Let K be a commutative ring with unity, let R be an associative K-algebra that is a finitely generated projective K-module, let Λ...

suppose $gamma$ is a graph with $v(gamma) = { 1,2, cdots, p}$and $ mathcal{f} = {gamma_1,cdots, gamma_p} $ is a family ofgraphs such that $n_j = |v(gamma_j)|$, $1 leq j leq p$. define$lambda = gamma[gamma_1,cdots, gamma_p]$ to be a graph withvertex set $ v(lambda)=bigcup_{j=1}^pv(gamma_j)$ and edge set$e(lambda)=big(bigcup_{j=1}^pe(gamma_j)big)cupbig(bigcup_{ijine(gamma)}{uv;uin v(gamma_i),vin ...

The main result of this paper gives necessary and sufficient conditions for the ^-primary part S(K)P of the Schur group S (K) to be induced from S (F)p for any subfield F of K where K is contained in Q (εn), under the restriction that εp2 is not in K if p > 2 and n is odd if p~2, where εn is a primitive nth root of unity. Moreover we completely answer the question: "When is SiQiεn + ε-)) induce...

A new approach for spacecraft absolute attitude estimation based on the unscented Kalman filter (UKF) is extended to relative attitude estimation and navigation. This approach for nonlinear systems has faster convergence than the approach based on the standard extended Kalman filter (EKF) even with inaccurate initial conditions in attitude estimation and navigation problems. The filter formulat...

Some complex quaternionic equations in the type AX - XB = C are investigated. For convenience, these equations were called generalized Sylvester-quaternion equations, which include the Sylvester equation as special cases. By the real matrix representations of complex quaternions, the necessary and sufficient conditions for the solvability and the general expressions of the solutions are obtained.

This paper discusses quaternion L geometric weighting averaging working on the multiplicative Lie group of nonzero quaternionsH∗, endowed with its natural bi-invariant Riemannian metric. Algorithms for computing the Riemannian L center of mass of a set of points, with 1 ≤ p ≤ ∞ (i.e., median, mean, L barycenter and minimax center), are particularized to the case of H∗. Two different approaches ...