TY - JOUR
T1 - Condition for the numerical range to contain an elliptic disc
AU - Gau, Hwa Long
AU - Wu, Pei Yuan
N1 - Funding Information:
Research partially supported by the National Science Council of the Republic of China. ∗Corresponding author. E-mail addresses: [email protected] (H.-W. Gau), [email protected] (P.Y. Wu).
PY - 2003/5/1
Y1 - 2003/5/1
N2 - For an n-by-n matrix A and an elliptic disc E in the plane, we show that the sum of the number of common supporting lines and the number of common intersection points to E and the numerical range W(A) of A should be at least 2n+1 in order to guarantee that E be contained in W(A). This generalizes previous results of Anderson and Thompson. As an application, our result is used to verify a special case of the Poncelet property conjecture.
AB - For an n-by-n matrix A and an elliptic disc E in the plane, we show that the sum of the number of common supporting lines and the number of common intersection points to E and the numerical range W(A) of A should be at least 2n+1 in order to guarantee that E be contained in W(A). This generalizes previous results of Anderson and Thompson. As an application, our result is used to verify a special case of the Poncelet property conjecture.
UR - http://www.scopus.com/inward/record.url?scp=0037400828&partnerID=8YFLogxK
U2 - 10.1016/S0024-3795(02)00548-7
DO - 10.1016/S0024-3795(02)00548-7
M3 - 期刊論文
AN - SCOPUS:0037400828
SN - 0024-3795
VL - 364
SP - 213
EP - 222
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
ER -