Line Segments of The Boundary of Numerical Range

• Main Authors: Meng-Yenan Cheng, 陳孟遠
• Other Authors: Hwa-Long Gau
• Format: Others
• Language: en_US
• Published: 2003
• Online Access: http://ndltd.ncl.edu.tw/handle/28446137991059320772

碩士 === 國立中央大學 === 數學研究所 === 91 === In this thesis, we consider the problem of characterizing the numerical ranges of 4 by 4 matrices which have line segments on its boundary. If pA is reducible, we will obtain the result what we want easily. Thus it is sufficient to consider the irreducibility of pA. In this case, we will give a sufficient and necessary condition for the numerical range of a 4 by 4 matrix with a line segment on its boundary. Moreover, we also give a criterion for the numerical range of a 4 by 4 matrix with a pair of parallel line segment on its boundary.