86 citations · 102 across the 21 of their papers we have counts for
21 papers
The determinant of the Laplacian matrix of a quaternion unit gain graph
Ivan I. Kyrchei, Eran Treister, Volodymyr O. Pelykh
A quaternion unit gain graph is a graph where each orientation of an edge is given a quaternion unit, and the opposite orientation is assigned the inverse of this quaternion unit.…
Determinantal representations of the weighted core-EP, DMP, MPD, and CMP inverses of matrices with quaternion and complex elements
Ivan I. Kyrchei
In this paper, we extend notions of the weighted core-EP right and left inverses, the weighted DMP and MPD inverses, and the CMP inverse to matrices over the quaternion skew field…
The quaternion core inverse and its generalizations
Ivan I. Kyrchei
In this paper we extend notions of the core inverse, core EP inverse, DMP inverse, and CMP inverse over the quaternion skew-field and get their determinantal represe…
Linear differential systems over the quaternion skew field
Ivan Kyrchei
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…
Explicit determinantal formulas for solutions to the generalized Sylvester quaternion matrix equation and its special cases
Ivan Kyrchei
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…
Cramer's rules for the solution to the two-sided restricted quaternion matrix equation
Ivan Kyrchei
Weighted singular value decomposition (WSVD) of a quaternion matrix and with its help determinantal representations of the quaternion weighted Moore-Penrose inverse have been deriv…