NUMERICAL RANGES AND NUMERICAL RADII OF PRODUCTS OF 3×3 MATRICES

• Main Authors: Ken-fu Lin, 林肯甫
• Other Authors: Hwa-long Gau
• Format: Others
• Language: en_US
• Published: 2015
• Online Access: http://ndltd.ncl.edu.tw/handle/er33ft

碩士 === 國立中央大學 === 數學系 === 103 === In this thesis, for any two 3-by-3 complex matrices A and B, we show that the necessary and sufficient conditions for the equality W(AB) = W(BA) to hold, where W() denotes the numerical range of a matrix, and the structure of A when w(A) =w (A2) = 1 and w (A3) < 1, where w() denotes the numerical radius of a matrix, and obtain the necessary and sufficient condition for the equality w(A B) = kAkw(B)to hold when A is a completely nonunitary contraction with kAk = 1, where k k denotes the usual operator norm of a matrix.