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...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Others |
| Language: | en_US |
| Published: |
2012
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| Online Access: | http://ndltd.ncl.edu.tw/handle/41186791618919990845 |
| Summary: | 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.
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