Invertibility criteria, resolvent and spectrum of linear operator matrix pencil
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Operator matrix pencils are very useful in many analysis problems. In particular, they are often used in studies of control systems with linear descriptors. Generalized eigenvalue problems of matrix pencils have drown gained interest for decades from mathematicians and engineers. The novelty of our work is to develop a new sufficient criteria to compute the eigenvalues of square operator matrix pencil defined with diagonal domain. Some spectral properties as well as practical criteria for computation of the resolvent form of square operator matrix pencil with diagonal domain will be discussed by exploiting this new technique.
Abstract
Operator matrix pencils are very useful in many analysis problems. In particular, they are often used in studies of control systems with linear descriptors. Generalized eigenvalue problems of matrix pencils have drown gained interest for decades from mathematicians and engineers. The novelty of our work is to develop a new sufficient criteria to compute the eigenvalues of square operator matrix pencil defined with diagonal domain. Some spectral properties as well as practical criteria for computation of the resolvent form of square operator matrix pencil with diagonal domain will be discussed by exploiting this new technique.