The Symmetry Of Numerical Range For Some Operators

This paper is divided into three chapters.The theoretical background and develop-ment of the numerical range of operator and the research of Drazin inverse of the linear operator are briefly outlined in the first chapter.In the second chapter,based on the sym-metry of the spectrum of operator with the imaginary axis,the real axis.and even the line through the origin,the symmetry of the numerical range quadratic numerical range for some operator(matrices)with the line through the origin is studied.the structrual charac-teristics of the operator is revealed,and the rationality of the resultis illustrated in terms of example.In the third chapter,under some condition,Drazin inverse representations of the combinations of linear operators are obtained,and the validity of the result is explained through the example...