Bibliographic Details
| Title: |
On numerical ranges of the compressions of normal matrices |
| Authors: |
Adam, Maria1 madam@ucg.gr |
| Source: |
Applied Mathematics & Computation. Jan2011, Vol. 217 Issue 9, p4699-4709. 11p. |
| Subjects: |
Numerical analysis, Matrices (Mathematics), Isometrics (Mathematics), Projective geometry, Boundary value problems, Mathematical analysis |
| Abstract: |
Abstract: For an n × n normal matrix A, whose numerical range NR[A] is a k-polygon (k ⩽ n), an n ×(k −1) isometry matrix P is constructed by a unit vector , and NR[P∗AP] is inscribed to NR[A]. In this paper, using the notations of NR[P∗AP] and some properties from projective geometry, an n × n diagonal matrix B and an n ×(k −2) isometry matrix Q are proposed such that NR[P∗AP] and NR[Q∗BQ] have as common support lines the edges of the k-polygon and share the same boundary points with the polygon. It is proved that the boundary of NR[P∗AP] is a differentiable curve and the boundary of the numerical range of a 3×3 matrix P∗AP is an ellipse, when the polygon is a quadrilateral. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
