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DOIONLINE NO - IJMAS-IRAJ-DOIONLINE-11824

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International Journal of Management and Applied Science (IJMAS)-IJMAS
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Volume Issue
Issue
Volume-4,Issue-4  ( Apr, 2018 )
Paper Title
Numerical Range of Linear Pencils
Author Name
Seyedehmasoumeh Vaseghrahimparvar, Hosseinali Abkenari
Affilition
department of applied Mathematic Azad university of Rasht-Rasht, Iran Associate Professor of Rasht university department of applied Mathematic-Rasht, Iran
Pages
46-47
Abstract
Let A, B be n X 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 – B, where  is a complex number. The numerical range of a linear pencil of a pair (A, B) is the set W(A, B) = {x * (A - B) x:x  Cn,  x  1,   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 - B, when one of the matrices A or B is Hermitian and C. we characterize it for small dimensions in terms of certain algebraic curves. For the case n = 2, the boundary generating curves are conics. For the case n = 3, all the possible boundary generating curves can be completely described by using Newton’s classification of cubic curves. The results are illustrated by numerical examples.
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