Cramer’s Rules for Some Hermitian Coquaternionic Matrix Equations

Abstract

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 of linear equations with Hermitian coquaternionic matrices of coefficients are obtained. Cramer's rule for a two-sided coquaternionic matrix equation AXB = D (with Hermitian A, B) is given as well.

Solution to Several Split Quaternion Matrix Equations

“…In conclusion, (2) is solvable if and only if (11) is solvable. In addition, we have proven that (2) can be constructed using the solution Y of (11) when ( 11) is solvable Remark 2.…”

“…Via direct computation, we can see that Ŷ = X τ is a solution to the real matrix Equation (11). Now, X τ satisfies…”

“…Jiang et al [10] studied the right eigenvalues and eigenvectors of split quaternion matrices and derived explicit formulas. Kyrchei [11] provided the original Cramer's rule for some Hermitian split matrix equations using noncommutative determinants. Wang et al [12] derived the singular value decomposition of a split quaternion matrix and considered the constraint least squares problem.…”

Generalized Split Quaternions and Their Applications on Non-Parabolic Conical Rotations

“…Split quaternions can be used to represent conical rotations on standard hyperboloids, which are spheres in three-dimensional Lorentzian geometry [12,20,21]. Some recent studies on split quaternions are also given in the reference section [22][23][24].…”