Spectral theory for self-adjoint quadratic eigenvalue problems - a review
نویسندگان
چکیده
منابع مشابه
Model-updating for self-adjoint quadratic eigenvalue problems
This paper concerns quadratic matrix functions of the form L(λ) = Mλ2 +Dλ+K where M,D,K are Hermitian n× n matrices with M > 0. It is shown how new systems of the same type can be generated with some eigenvalues and/or eigenvectors updated and this is accomplished without “spill-over” (i.e. other spectral data remain undisturbed). Furthermore, symmetry is preserved. The methods also apply for H...
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This agrees with the definition of the spectrum in the matrix case, where the resolvent set comprises all complex numbers that are not eigenvalues. In terms of its spectrum, we will see that a compact operator behaves like a matrix, in the sense that its spectrum is the union of all of its eigenvalues and 0. We begin with the eigenspaces of a compact operator. We start with two lemmas that we w...
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A system is defined to be an n× n matrix function L(λ) = λ2M + λD +K where M, D, K ∈ Cn×n and M is nonsingular. First, a careful review is made of the possibility of direct decoupling to a diagonal (real or complex) system by applying congruence or strict equivalence transformations to L(λ). However, the main contribution is a complete description of the much wider class of systems which can be...
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The spectral theorem for commuting self-adjoint operators along with the associated functional (or operational) calculus is among the most useful and beautiful results of analysis. It is well known that forming a functional calculus for noncommuting self-adjoint operators is far more problematic. The central result of this paper establishes a rich functional calculus for any finite number of no...
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ژورنال
عنوان ژورنال: The Electronic Journal of Linear Algebra
سال: 2021
ISSN: 1081-3810
DOI: 10.13001/ela.2021.5361