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(The) numerical range of the Jordan block on 3-dimensional space
- Title
- (The) numerical range of the Jordan block on 3-dimensional space
- Authors
- 박미례
- Issue Date
- 2002
- Department/Major
- 대학원 수학과
- Keywords
- Jordan block; 3-dimensional space; 수학
- Publisher
- 이화여자대학교 대학원
- Degree
- Master
- Abstract
- 이 논문에서는 어떤 작용소 T의 numerical range의 여러 가지 성질들에 대하여 공부한다. 특히, 3차원 공간상에서 작용소 T의 Jordan form에 대한 numerical range를 특성화 한다;In this paper, we study some properties of numerical range for any operator T . In particular, we focus on the numerical ranges of Jordan forms of an operator T on a 3-dimensional space. This characterization depends on the diagonalization of an operator T on a 3-dimensional space. In fact, if T ∈ M_(3) and T_(J) is the Jordan form of T , we show that W(T_(J)) = conv(σ(T_(J))) when T is diagonalizable. Moreover we calculate several forms of the numerical ranges of a non-diagonalizable operator.
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