Paper Title :Numerical Range of Linear Pencils

Author :Seyedehmasoumeh Vaseghrahimparvar, Hosseinali Abkenari

Article Citation :Seyedehmasoumeh Vaseghrahimparvar ,Hosseinali Abkenari , (2018 ) " Numerical Range of Linear Pencils " , International Journal of Management and Applied Science (IJMAS) , pp. 46-47, Volume-4,Issue-4

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.

Type : Research paper

Published : Volume-4,Issue-4

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