Properties And Representations Of Generalized Inverse On Algebraic Perturbation And Minimal Property Of Condition Number On Drazin Inverse

The representation and calculation of generalized inverse matrices is an important topic in the theory of generalized inverse. Since its high value in the field of both theotical research and practical use, many scholars have done much research on it. (Refs: [1⁶]etc.)In the year of 1974, J.R.Bunch and D.J.Rose found a new way called algebraic perturbation method for solving nonsingular linear equations. After then, L.B.Rall, Y.L. Chen and J. Ji have also done a large amount of work on it with results in properties of linear operator on Banach space, {1}-inverse, {1,2}-inverse and .A_T,S²-inverse of matrices. The third charpt of this paper is going to discuss the properties and representations on algebraic perturbation of generalized Bott-Duffin inverse and weighted Drazin inverse.In term of the important practical applications of division ring to engineering and physics, in the forth charpt, we give some new results in P-division ring on algebraic perturbation theory.Condition number is one of the most important indecies which are used to measure sensitation of matrix against perturbation. In the fivth charpt, we obtain some properties of matrix when its condition number on Drazin inverse is minimal.And flnaly, we will find some properties of nonnegative matrices which having same nonnegative group inverse and M-P inverse.