Abstract
Let J be an involutive Hermitian matrix with signature (t, n − t), 0 ≤ t ≤ n, that is, with t positive and n − t negative eigenvalues. The Krein space numerical range of a complex matrix A of size n is the collection of complex numbers of the form ξ ∗ JA ξ ξ∗ Jξ ,w ithξ ∈ C n and ξ ∗ Jξ � . In this note, a class of tridiagonal matrices with hyperbolical numerical range is investigated. A Matlab program is developed to generate Krein spaces numerical ranges in the finite dimensional case.
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