Dual Group Inverse And Dual Drazin Inverse Of Dual Matrices And Their Applications In Solving Linear Dual Equations

Dual generalized inverses have attracted extensive attentions in the past three decades because of their applications in many fields,such as mechanical systems,robotics and kinematic analysis.However,unlike real matrices,dual generalized inverses of dual matrices may not exist.Therefore,it is significant and interesting to study the existence and expressions of dual generalized inverses.In this thesis,two kinds of dual generalized inverses,namely the dual group inverse and the dual Drazin inverse are studied.Some necessary and sufficient conditions for a dual matrix to have the dual group inverse and the dual Drazin inverse are given.If these two dual generalized inverses exists,then compact formulas and effective methods for the computations of the dual group inverse and the dual Drazin inverse are given.In addition,the results of the dual group inverse and the dual Drazin inverse are applied to systems of linear dual equations.The solutions,least-squares solutions and minimum P-norm solutions of systems of linear dual equations are given by introducing the dual-group inverse solution and the dual Drazin-inverse solution.Some numerical examples are given to illustrate the results.