Numerical range

The numerical range of an operator

A

is

N (A) = {⟨ ψ ∣ A ∣ ψ ⟩ : ∥ ψ ∥ = 1} .

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- Numerical range of a normal matrix Numerical range

Numerical range of a normal matrix

For a finite-dimensional normal matrix, the numerical range is the convex hull of its eigenvalues.

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The numerical range is an important concept in functional analysis and operator theory.

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