The Numerical Field And Numerical Radius Of Several Matrix Operators

In this paper, we firstly gives the operator the value domain basic definitions, on the basis of the next few chapters give a few classes Operators of numerical range and numerical radius, the last we do the research domain.This paper is divided into three chapters:In Chapter 1, we give the definition and basic properties of the numerical range. We also show that the numerical range of a linear operator is a convex subset.In Chapter 2, we first give the definition 2×2 matrix operator where H is a Hilbert space. Then using the oval theorem, we show that the numerical range of 2×2 matrix operator is elliptical. We give some properties of its numerical radius. We also show thatWe also consider the numerical range and numerical radius of n×n operator matrix. We say is a tridiagonal matrix. We also consider the numerical range and numerical radius of the three-diagonal matrix.In Chapter 3, we first give the definition of C-numerical range, and then by 2×2 matrix operator summary field in front of common values, then we study 2×2 matrix operator C-numerical range, and gives the conclusions.