臺灣博碩士論文加值系統

對於橢圓形數值域（Numerical Range）之四階方陣 而言，其C_R(A)可能的情形為兩點及一橢圓或者為兩個橢圓；我們分別就此兩種情形，討論其與四階方陣中的元素及特徵值（Eigenvalues）之間的關係，並且得到兩者共存的條件。接下來，我們對形如（4﹒2）的四階方陣做相同的討論，從而得到更一步的結果。

The aim of this thesis is to provide characterizations of a 4x4 matrix A with
elliptic numerical range. We will express the conditions in terms of the eigenvalues and entries of A. These characterizations will be useful to construct a 4x4 matrix with an elliptic numerical range.

1.Introduction..................................................1
2.Preliminaries.................................................1
2.1 Basic Properties of Numerical Range.......................1
2.2 Kippenhahn Curve..........................................3
3.2x2 and 3x3 Matrices..........................................6
4.4x4 Matrices..................................................9
References...................................................31

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