Kyrchei I. Generalized inverse matrices over the quaternion skew field and their applications

The thesis is devoted to generalized inverse matrices over the quaternion skew field, first of all to their determinantal representations, and their applications to componentwise sollving of quaternion matrix equations. Determinantal representations of quaternion generalized inverse matrices of Moore-Penrose, Drazin, and their weighted ones are constructed using noncommutative row and column determinants, the theory of which was developed by the applicant in his Ph.D. thesis. Determinantal representations of the quaternion core inverse matrix and its generalizations are obtained. Analogues of Cramer's rule of quaternion generalized matrix Sylvester equations and a system of two-sided matrix equations, all their partial cases, and special cases with * -hermitian and η-hermitian are constructed. Analogues of Cramer's rule of the Drazin inverse solutions, weighted Moore-Penrose and Drazin inverse solutions to the two-sided matrix equation with corresponding restrictions are derived. Determinantal representations of solutions of some quaternion singular differential matrix equations and matrix minimization problems are obtained.