The Boundary of Numerical Ranges

The Boundary of Numerical Ranges

碩士 === 東吳大學 === 數學系 === 100 === In this paper we study the boundary of the numerical ranges. Let S = {x : x^*x = 1, x E C^n}. The numerical range of an n × n complex matrix A is defined to be the set W(A) = {x^*Ax : x 2 S}. We list some fundamental properties in section 1. In section 2, we discuss t...

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Main Authors: Wen-chih Liu, 劉文智
Other Authors: Mao-Ting Chien
Format: Others
Language:en_US
Published: 2012
Online Access:http://ndltd.ncl.edu.tw/handle/41186791618919990845
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spelling ndltd-TW-100SCU054790012015-10-13T21:12:27Z http://ndltd.ncl.edu.tw/handle/41186791618919990845 The Boundary of Numerical Ranges The Boundary of Numerical Ranges Wen-chih Liu 劉文智 碩士 東吳大學 數學系 100 In this paper we study the boundary of the numerical ranges. Let S = {x : x^*x = 1, x E C^n}. The numerical range of an n × n complex matrix A is defined to be the set W(A) = {x^*Ax : x 2 S}. We list some fundamental properties in section 1. In section 2, we discuss the angle between x Ay and y Ax when x Ax lies on the boundary of W(A). In section 3, we study properties of corner x^*Ax of W(A). Finally we give some special geometry in section 4. i Mao-Ting Chien 簡茂丁 2012 學位論文 ; thesis 20 en_US
collection NDLTD
language en_US
format Others
sources NDLTD
description 碩士 === 東吳大學 === 數學系 === 100 === In this paper we study the boundary of the numerical ranges. Let S = {x : x^*x = 1, x E C^n}. The numerical range of an n × n complex matrix A is defined to be the set W(A) = {x^*Ax : x 2 S}. We list some fundamental properties in section 1. In section 2, we discuss the angle between x Ay and y Ax when x Ax lies on the boundary of W(A). In section 3, we study properties of corner x^*Ax of W(A). Finally we give some special geometry in section 4. i
author2 Mao-Ting Chien
author_facet Mao-Ting Chien
Wen-chih Liu
劉文智
author Wen-chih Liu
劉文智
spellingShingle Wen-chih Liu
劉文智
The Boundary of Numerical Ranges
author_sort Wen-chih Liu
title The Boundary of Numerical Ranges
title_short The Boundary of Numerical Ranges
title_full The Boundary of Numerical Ranges
title_fullStr The Boundary of Numerical Ranges
title_full_unstemmed The Boundary of Numerical Ranges
title_sort boundary of numerical ranges
publishDate 2012
url http://ndltd.ncl.edu.tw/handle/41186791618919990845
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AT wenchihliu boundaryofnumericalranges
AT liúwénzhì boundaryofnumericalranges
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