We present some practical necessary and sufficient conditions for the existence of an η-(anti-
) Hermitian solution to a constrained Sylvester-type generalized commutative quaternion …

This survey provides an overview of several powerful real and complex representations of
matrices over quaternion algebras including split quaternions and biquaternions as well as …

In this study, we show that the elliptic biquaternion algebra is algebraically isomorphic to the
2*2 total elliptic matrix algebra and so, we get a faithful 2*2 elliptic matrix representation of …

In this paper, the concept of the quaternionic adjoint matrix χ _A χ A of an elliptic
biquaternion matrix A is introduced, which enable one to discuss the elliptic biquaternion …

In this paper, we introduce the definition of the generalized reduced biquaternions and
propose a real representation of a generalized reduced biquaternion matrix. By using the …

In this study, we obtain the real representations of elliptic biquaternion matrices. Afterwards,
with the aid of these representations, we develop a general method to solve the linear matrix …

This chapter is devoted to the survey of quaternion restricted two-sided matrix equation
AXB= D and approximation problems related with it. Unique solutions to the considered …

In this paper, we propose to write the generalization of gravity, including the Proca‐type and
gravitomagnetic monopole terms through a new algebraic structure elliptic biquaternions …

In the early 2000s, the geometry of a one-parameter family of generalized complex number
systems was studied (Math. Mag. 77 (2)(2004)). This family is denoted by Cp. It is well …

AF Horadam defined the complex Fibonacci numbers and Fibonacci quaternions in the
middle of the 20th century. Half a century later, S. Hal\ic\i introduced the complex Fibonacci …