Abstract
The rank- k-numerical range of an n × n matrix A is defined as Λ k ( A ) = { λ ∈ C : PAP = λ P for some rank k orthogonal projection P } . This study presents a method to generate the boundary of Λ k ( A ) , and examines the flat portions of the boundary of the rank- k-numerical range of a matrix associated with a roulette curve. A sufficient condition is given to ensure that the rank- k-numerical range is not attainable by a classical numerical range.
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