𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Numerical ranges as circular discs

✍ Scribed by Pei Yuan Wu

Book ID
104001237
Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
206 KB
Volume
24
Category
Article
ISSN
0893-9659

No coin nor oath required. For personal study only.

✦ Synopsis

We prove that if a finite matrix A of the form

is contained in the closed circular disc D centered at a and βˆ‚W (A) ∩ βˆ‚D has more than nm points, then W (A) = D and a is an eigenvalue of C .

To prove this theorem, we need the following lemma. Let D = {z ∈ C :

πŸ“œ SIMILAR VOLUMES

Numerical ranges and GerΕ‘gorin discs
Numerical ranges and GerΕ‘gorin discs
✍ Chi-Tung Chang; Hwa-Long Gau; Kuo-Zhong Wang; Pei Yuan Wu πŸ“‚ Article πŸ“… 2013 πŸ› Elsevier Science 🌐 English βš– 528 KB
On matrices whose numerical ranges have
On matrices whose numerical ranges have circular or weak circular symmetry
✍ Bit-Shun Tam; Shangjun Yang πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 205 KB

In , among other equivalent conditions, it is proved that a square complex matrix A is permutationally similar to a block-shift matrix if and only if for any complex matrix B with the same zero pattern as A, W (B), the numerical range of B, is a circular disk centered at the origin. In this paper, w