The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...

an involution or anti-involution is a self-inverse linear mapping. in this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. moreover, properties and geometrical meanings of these matrices will be given as reflections in r^3.

An involution or anti-involution is a self-inverse linear mapping. In this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. Moreover, properties and geometrical meanings of these matrices will be given as reflections in R^3.

In this paper, a series of bicomplex representation methods of quaternion division algebra is introduced. We present a new multiplication concept of quaternion matrices, a new determinant concept, a new inverse concept of quaternion matrix and a new similar matrix concept. Under the new concept system, many quaternion algebra problems can be transformed into complex algebra problems to express ...

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 study, we develop a general method to solve the linear elliptic quaternionic matrix equations by means of real representation quaternion matrices. A pseudocode for our approach that provides solution is expressed. Moreover, apply well-known Slyvester and Kalman Yakubovich over algebra.

In this note‎, ‎we obtain some singular values inequalities for positive semidefinite matrices by using block matrix technique‎. ‎Our results are similar to some inequalities shown by Bhatia and Kittaneh in [Linear Algebra Appl‎. ‎308 (2000) 203-211] and [Linear Algebra Appl‎. ‎428 (2008) 2177-2191]‎.