Numerical ranges and Geršgorin discs
✍ Scribed by Chi-Tung Chang; Hwa-Long Gau; Kuo-Zhong Wang; Pei Yuan Wu
- Book ID
- 119317706
- Publisher
- Elsevier Science
- Year
- 2013
- Tongue
- English
- Weight
- 528 KB
- Volume
- 438
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
We prove that if a finite matrix A of the form is contained in the closed circular disc D centered at a and ∂W (A) ∩ ∂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 :
For complex square matrices, the Levy-Desplanques theorem asserts that a strictly diagonally dominant matrix is invertible. The well-known Geršgorin theorem on the location of eigenvalues is equivalent to this. In this article, we extend the Levy-Desplanques theorem to an object in a Euclidean Jorda