Let A,B be n×n (complex) matrices. We are mainly interested in the study of the structure of the spectrum of a linear pencil, that is, a pencil of the form A−λB, where λ is a complex number. Our main purpose is to obtain spectral inclusion regions for the pencil based on numerical range. The numerical range of a linear pencil of a pair (A, B) is the set W(A,B) = {x∗(A−λB)x : x ∈ Cn,∥x∥ = 1,λ ∈ C}. The numerical range of linear pencils with hermitian coefficients was studied by some authors. We are mainly interested in the study of the numerical range of a linear pencil, A − λB, when one of the matrices A or B is Hermitian and λ ∈ C. We characterize it for small dimensions in terms of certain algebraic curves. The results are illustrated by numerical examples. Fatemeh Esmaeili Taheri is a student of the Joint PhD Program in Mathematics UC|UP working at University of Coimbra in the area of "Algebra and Combinatorics" under the supervision of Prof. Natália Bebiano. The seminar takes place in PORTO.
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