On the hyperbolicity of the Krein space numerical range
Natália Bebiano, Rute Lemos, Graça Soares · Linear and Multilinear Algebra · 2023
In this paper a necessary and sufficient condition for hyperbolicity of the indefinite numerical range is established. As a consequence, an indefinite version of Brown–Spitkovsky theorem stating the ellipticity of the numerical range of certain tridiagonal matrices is revisited. This result leads to necessary and sufficient conditions for hyperbolicity of indefinite numerical ranges of new classes of tridiagonal matrices.