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 …

In this paper, we propose a definition of block tensors and the real representation of tensors.
Equipped with the simplification method, ie, the real representation along with the MP …

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

ABSTRACT BCTRU is a newly generated multi-dimensional NTRU like public key
cryptosystem. It is based on a newborn algebraic structure utilized instead of the classical …

In this paper, using the real representation method, we study the reduced biquaternion
matrix equation AX= B AX= B. Taking advantage of the special structure of real …

In this work, we have established universal similarity factorization equalities over the
commutative quaternions and their matrices. Based on these equalities, real matrix …

Compared to quaternions, reduced biquaternions satisfy the multiplication commutative rule
and are widely employed in applications such as image processing, fuzzy recognition …