Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6418805 | Journal of Mathematical Analysis and Applications | 2014 | 5 Pages |
Abstract
Let A=(A11A12A21A22)âMn, where A11âMm with m⩽n/2, be such that the numerical range of A lies in the set {eiÏzâC:|âz|⩽(âz)tanα}, for some Ïâ[0,2Ï) and αâ[0,Ï/2). We obtain the optimal containment region for the generalized eigenvalue λ satisfyingλ(A1100A22)x=(0A12A210)xfor some nonzero xâCn, and the optimal eigenvalue containment region of the matrix ImâA11â1A12A22â1A21 in case A11 and A22 are invertible. From this result, one can show |det(A)|⩽sec2m(α)Ã|det(A11)det(A22)|. In particular, if A is an accretive-dissipative matrix, then |det(A)|⩽2m|det(A11)det(A22)|. These affirm some conjectures of Drury and Lin.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Chi-Kwong Li, Nung-Sing Sze,