Normality and the numerical range
Copyright policy )Normality and the numerical range
AbstractIt is well known that if A is an n by n normal matrix, then the numerical range of A is the convex hull of its spectrum. The converse is valid for n ⩽ 4 but not for larger n. In this spirit a characterization of normal matrices is given only in terms of the numerical range. Also, a characterization is given of matrices for which the numerical range coincides with the convex hull of the spectrum. A key observation is that the eigenvectors corresponding to any eigenvalue occuring on the boundary of the numerical range must be orthogonal to eigenvectors corresponding to all other eigenvalues.
- National Institute of Standards and Technology United States
- University of Maryland, College Park United States
- University of Maryland, College Park United States
Numerical Analysis, Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology, Quadratic and bilinear forms, inner products, Inequalities involving eigenvalues and eigenvectors
Numerical Analysis, Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology, Quadratic and bilinear forms, inner products, Inequalities involving eigenvalues and eigenvectors
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