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 …

In this paper, we propose three real representations of a generalized Segre quaternion
matrix. We establish necessary and sufficient conditions for the existence of the η-anti …

This paper considers the Hermitian solutions of a new system of commutative quaternion
matrix equations, where we establish both necessary and sufficient conditions for the …

In this paper, we propose a necessary and sufficient condition for the solvability to a system
of matrix equations over the commutative quaternion ring, and establish an expression of its …

Quaternions are a four-dimensional hypercomplex number system discovered by Hamilton
in 1843 and next intensively applied in mathematics, modern physics, computer graphics …

In this study, we derive the expressions of the minimal norm least-squares solution for the
reduced biquaternion (RB) matrix equation AX= B by using the e 1− e 2 form of RB matrices …

Dual generalized commutative quaternions have broad application prospects in many fields.
Additionally, the matrix equation AXB= C has important applications in mathematics and …

By means of a complex representation of a commutative quaternion matrix, the singular
value decomposition and the generalized inverse problems of a commutative quaternion …

This paper, by means of two matrix representations of a commutative quaternion matrix,
studies the relationship between the solutions of commutative quaternion equality …

Due to the rise of commutative quaternion in Hopfield neural networks, digital signal, and
image processing, one encounters the approximate solution problems of the commutative …