Remarkably simple closed-form expressions for the elements of the groups SU(n), SL(n,R), and SL(n,C) with n = 2, 3, and 4 are obtained using linear functions of biquaternions instead of n × n matrices. These representations do not directly generalize to SU(n > 4). However, the quaternion methods used are sufficiently general to find applications in quantum chromodynamics and other problems whic...

The random matrix ensembles are applied to the quantum statistical systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the systems act on these Hilbert spaces and they are treated as random matrices in generic bases of the eigenfunctions. The random eigenproblems are presented an...

Tensor, matrix and quaternion formulations of Dirac-Kähler equation for massive and massless fields are considered. The equation matrices obtained are simple linear combinations of matrix elements in the 16-dimensional space. The projection matrix-dyads defining all the 16 independent equation solutions are found. A method of computing the traces of 16-dimensional Petiau-Duffin-Kemmer matrix pr...

The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the systems act on these Hilbert spaces and they are treated as random matrices in generic bases of the eigenfunctions. The random e...

• Vectorspaces over division rings • Matrices, opposite rings • Semi-simple modules and rings • Semi-simple algebras • Reduced trace and norm • Other criteria for simplicity • Involutions • Brauer group of a field • Tensor products of fields • Crossed product construction of simple algebras • Cyclic algebra construction of simple algebras • Quaternion algebras • Examples • Unramified extensions...

1 Abstract The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the systems act on these Hilbert spaces and they are treated as random matrices in generic bases of the eigenfunctions. T...

The random matrix ensembles are applied to the quantum chaotic systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the systems act on these Hilbert spaces and they are treated as random matrices in generic bases of the eigenfunctions. The random eigenproblems are presented and so...

Abstract The solvability of several new constrained quaternion matrix equations is investigated, and their unique solutions are presented in terms the weighted MPD inverse DMP suitable matrices. It interesting to consider some exceptional cases these corresponding solutions. Determinantal representations for as mentioned earlier established sums appropriate minors. In order illustrate obtained ...

Reducible matrices are closely associated with the connection of directed graph and can be used in stochastic processes, biology others. In this paper, we investigate reducible solution to a system matrix equations over Hamilton quaternion algebra. We establish necessary sufficient conditions for have derive formula general when it is solvable. Finally, present numerical example illustrate main...