We study quaternionic linear equations of type λm(x) := m j=1 b j xc j = e with quaternionic constants b j , c j , e and arbitrary positive integer m. For m = 2 the resulting equation is called Sylvester's equation. For this case a complete solution (solution formula, determination of null space) will be given. For the general case we show that the solution can be found by a corresponding matri...

We propose a general paradigm for generating optimal coordinate frame fields that may be exploited to annotate and display curves and surfaces. Parallel-transport framings, which work well for open curves, generally fail to have desirable properties for cyclic curves and for surfaces. We suggest that minimal quaternion measure provides an appropriate generalization of parallel transport. Our fu...

In this paper, the fuzzy matrix equation $Awidetilde{X}B=widetilde{C}$ in which $A,B$ are $n times n$crisp matrices respectively and $widetilde{C}$ is an $n times n$ arbitrary LR fuzzy numbers matrix, is investigated. A new numerical procedure for calculating the fuzzy solution is designed and a sufficient condition for the existence of strong fuzzy solution is derived. Some examples are ...

Finding the rotational matrix that minimizes the sum of squared deviations between two vectors is an important problem in bioinformatics and crystallography. Traditional algorithms involve the inversion or decomposition of a 3 x 3 or 4 x 4 matrix, which can be computationally expensive and numerically unstable in certain cases. Here, we present a simple and robust algorithm to rapidly determine...

in this article we study steensen method to solve nonlinear matrix equation x+a^t x^(-1) a=q, when a is a normal matrix. we establish some conditions that generate a sequence of positive denite matrices which converges to solution of this equation.

The purpose of this paper is to compare performances between stabilization algorithms quaternion plus attitude rate feedback and rotation matrix for an Earth-pointing spacecraft with magnetorquers as the only torque actuators. From a mathematical point view, important difference two stabilizing laws that can exhibit undesired behavior known unwinding phenomenon. A numerical case study considere...

In this study, generalized k-order Fibonacci hybrid quaternion is defined. We give recurrence relation, generating function, the summation formula and some properties for these quaternions. Furthermore, matrix representation quaternions determined. The Q_k defined numbers given By means of another matrices, several identities are also obtained.

The scalar–vector representation is used to derive a simple algorithm to obtain the roots of a quadratic quaternion polynomial. Apart from the familiar vector dot and cross products, this algorithm requires only the determination of the unique positive real root of a cubic equation, and special cases (e.g., double roots) are easily identified through the satisfaction of algebraic constraints on...

Recent developments in quaternion-valued widely linear processing have established that the exploitation of complete second-order statistics requires consideration of both the standard covariance and the three complementary covariance matrices. Although such matrices have a tremendous amount of structure and their decomposition is a powerful tool in a variety of applications, the noncommutative...

In this paper, the quaternion Bessel-Fourier moments are introduced. The significance of phase information in quaternion Bessel-Fourier moments is investigated and an accurate estimation method for rotation angle is described. Furthermore, a new set of invariant descriptors based on the magnitude and the phase information of quaternion Bessel-Fourier moments is derived. Experimental results sho...