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Krein spaces numerical ranges and their computer generation

2008
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The Electronic Journal of Linear Algebra
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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 * JAξ ξ * Jξ , with ξ ∈ C n and ξ * Jξ = 0. 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.

doi:10.13001/1081-3810.1258
fatcat:yvpq4ghe6ndjfkdmgxdobamvaq