We give a simple derivation of all n-point densities for the eigenvalues of the real Ginibre ensemble with even dimension N as quaternion determinants. A very simple symplectic kernel governs both, the real and complex correlations. 1-and2-point correlations are discussed in more detail. Scaling forms for large dimension N are derived. PACS numbers: 0250.-r, 0540.-a, 75.10.Nr Submitted to: J. P...

We consider when the quaternion matrix equation AXB+CXD=E has a reflexive (or anti-reflexive) solution with respect to given generalized reflection matrix. adopt real representation method derive solutions it is solvable. Moreover, we obtain explicit expressions of least-squares solutions.

We construct a new family of compact orbifolds O(Θ) with a positive self dual Einstein metric and a one-dimensional group of isometries. Together with another family, introduced in [6] and here denoted by O(Ω), these examples classify all 4-dimensional orbifolds that are quaternion Kähler quotients by a torus of real Grassmannians.

In this paper, we present some applications of quaternions and octonions. We present the real matrix representations for complex octonions and some of their properties which can be used in computations where these elements are involved. Moreover, we give a set of invertible elements in split quaternion algebras and in split octonion algebras.

The coincidence site lattice (CSL) problem and its generalization to Z-modules in Euclidean 3-space is revisited, and various results and conjectures are proved in a unified way, by using maximal orders in quaternion algebras of class number 1 over real algebraic number fields.

We present explicit formulas for the distributions of the extreme eigenvalues of the β–Jacobi random matrix ensemble in terms of the hypergeometric function of a matrix argument. For β = 1, 2, 4, these formulas specialize to the well-known real, complex, and quaternion Jacobi ensembles, respectively.

In this paper, we investigate a system of twelve quaternion matrix equations. Using the real representation matrix, first derive least-squares solution with least norm to system. Meanwhile, establish solvability conditions and an expression general when it is consistent.

For any Eichler order O(D,N) of level N in an indefinite quaternion algebra of discriminant D there is a Fuchsian group Γ(D,N) ⊆ SL(2,R) and a Shimura curve X(D,N). We associate to O(D,N) a set H(O(D,N)) of binary quadratic forms which have semi-integer quadratic coefficients, and we develop a classification theory, with respect to Γ(D,N), for primitive forms contained in H(O(D,N)). In particul...

This paper proposesa new class of unit quaternion curves in SO(3). A general method is developed that transforms a curve in R3 (defined as a weighted sum of basis functions) into its unit quaternion analogue in SO(3). Applying the method to well-known spline curves (such as Bézier, Hermite, and B-spline curves), we are able to construct various unit quaternion curves which share many important ...