We introduce three universality classes of chiral random matrix ensembles with a nonzero chemical potential and real, complex or quaternion real matrix elements. In the thermodynamic limit we find that the distribution of the eigenvalues in the complex plane does not depend on the Dyson index, and is given by the solution proposed by Stephanov. For a finite number of degrees of freedom, N , we ...

We examine computational problems on quaternion matrix and rotation semigroups. It is shown that in the ultimate case of quaternion matrices, in which multiplication is still associative, most of the decision problems for matrix semigroups are undecidable in dimension two. The geometric interpretation of matrix problems over quaternions is presented in terms of rotation problems for the 2 and 3...

In this paper, we present results on the implementation of a hierarchical quaternion based attitude and trajectory controller for manual and autonomous flights of quadrotors. Unlike previous papers on using quaternion representation, we use the nonlinear complementary filter that estimates the attitude in quaternions and as such does not involve Euler angles or rotation matrices. We show that f...

We treat the quaternionic Fourier transform (QFT) applied to quaternion fields and investigate QFT properties useful for applications. Different forms of the QFT lead us to different Plancherel theorems. We relate the QFT computation for quaternion fields to the QFT of real signals. We research the general linear (GL) transformation behavior of the QFT with matrices, Clifford geometric algebra ...

In this paper, we established the connection between generalized quaternion algebra and real (complex) matrix algebras by using Hamilton operators. We obtained complex matrices corresponding to basis of quaternions. Also, investigated features matrices. get Pauli Then, have shown that produced these is isomorphic Clifford Cl(E_αβ^3) space E_αβ^3.
 Finally, studied relations among symplecti...

In this paper, we study the bisymmetric and skew solutions of quaternion generalized Lyapunov equation. With help semi-tensor product matrices, some new conclusions on expansion rules row column matrix matrices are proposed applied to calculation Using H-representation method, independent elements extracted according structural characteristics matrix, so as simplify operation process. Finally, ...