Geometry of the numerical range of matrices
Copyright policy )Geometry of the numerical range of matrices
AbstractSome techniques for the study of the algebraic curve C(A) which generates the numerical range W(A) of an n×n matrix A as its convex hull are developed. These enable one to give an explicit point equation of C(A) and a formula for the curvature of C(A) at a boundary point of W(A). Applied to the case of a nonnegative matrix A, a simple relation is found between the curvature of the function Φ(A)=p((1−α)A+ αAT) (p being the Perron root) at α=12 and the curvature of W(A) at the Perron root of 12(A+AT). A connection with 2-dimensional pencils of Hermitian matrices is mentioned and a conjecture formulated.
- Auburn University United States
- Auburn University at Montgomery United States
- Czech Academy of Sciences Czech Republic
- Auburn University System United States
Numerical Analysis, Algebra and Number Theory, algebraic curve which generates the numerical range of an nxn matrix, Norms of matrices, numerical range, applications of functional analysis to matrix theory, Discrete Mathematics and Combinatorics, Geometry and Topology, Perron root
Numerical Analysis, Algebra and Number Theory, algebraic curve which generates the numerical range of an nxn matrix, Norms of matrices, numerical range, applications of functional analysis to matrix theory, Discrete Mathematics and Combinatorics, Geometry and Topology, Perron root
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