Related papers: Cramer rule over quaternion skew field
Determinantal representation of the Moore-Penrose inverse over the quaternion skew field is obtained within the framework of a theory of the column and row determinants. Using the obtained analogs of the adjoint matrix, we get the Cramer…
Cramer's rules for some left, right and two-sided quaternion matrix equations are obtained within the framework of the theory of the column and row determinants.
In this paper properties of the determinant of a Hermitian matrix are investigated, and determinantal representations of the inverse of a Hermitian coquaternionic matrix are given. By their using, Cramer's rules for left and right systems…
Within the framework of the theory of the column and row determinants, we obtain determinantal representations of the Drazin inverse for Hermitian matrix over the quaternion skew field. Using the obtained determinantal representations of…
Within the framework of the theory of the column and row determinants, we obtain new determinantal representations of the W-weighted Drazin inverse over the quaternion skew field. We give determinantal representations of the W-weighted…
Weighted singular value decomposition (WSVD) and a representation of the weighted Moore-Penrose inverse of a quaternion matrix by WSVD have been derived. Using this representation, limit and determinantal representations of the weighted…
By using determinantal representations of the W-weighted Drazin inverse previously obtained by the author within the framework of the theory of the column-row determinants, we get explicit formulas for determinantal representations of the…
Within the framework of the theory of quaternion column-row determinants and using determinantal representations of the Moore-Penrose inverse previously obtained by the author, we get explicit determinantal representation formulas of…
A basic theory on the first order right and left linear quaternion differential systems (LQDS) is given systematic in this paper. To proceed the theory of LQDS we adopt the theory of column-row determinants recently introduced by the…
We introduce a class of rings using which we define the concept of skew regularity for quaternion-valued functions over quaternions. It is shown that the notion of skew regularity coincides with the concept of slice regularity over…
Linear algebra is usually defined over a field such as the reals or complex numbers. It is possible to extend this to skew fields such as the quaternions. However, to the authors' knowledge there is no commonly accepted notation of linear…
In this article, we introduce determinantal representations of the Moore - Penrose inverse and the Drazin inverse which are based on analogues of the classical adjoint matrix. Using the obtained analogues of the adjoint matrix, we get…
Within the framework of the theory of the column and row determinants, we obtain explicit representation formulas (analogs of Cramer's rule) for the minimum norm least squares solutions of quaternion matrix equations ${\bf A} {\bf X} = {\bf…
Weighted singular value decomposition (WSVD) of a quaternion matrix and with its help determinantal representations of the quaternion weighted Moore-Penrose inverse have been derived recently by the author. In this paper, using these…
We complete all local spinor norm computations for quaternionic skew-hermitian forms over the field of rational numbers. Examples of class number computations are provided.
In this paper we extend notions of the core inverse, core EP inverse, DMP inverse, and CMP inverse over the quaternion skew-field ${\mathbb{H}}$ and get their determinantal representations within the framework of the theory of column-row…
Quadratic descent of hermitian and skew hermitian forms over division algebras with involution of the first kind in arbitrary characteristic is investigated and a criterion, in terms of systems of quadratic forms, is obtained. A refined…
In this study, we introduce the concept of commutative quaternions and commutative quaternion matrices. Firstly, we give some properties of commutative quaternions and their Hamilton matrices. After that we investigate commutative…
We investigate the a{\pm}ne circle geometry arising from a quaternion skew field and one of its maximal commutative subfields.
The theory of the column-row determinants has been considered for matrices over a non-split quaternion algebra. In this paper the concepts of column-row determinants are extending to a split quaternion algebra. New definitions of the column…