Editing Spectral theory (section)

{{Short description|Collection of mathematical theories}}
In [[mathematics]], '''spectral theory''' is an inclusive term for theories extending the [[eigenvector]] and [[eigenvalue]] theory of a single [[square matrix]] to a much broader theory of the structure of [[operator (mathematics)|operator]]s in a variety of [[mathematical space]]s.<ref name="Dieudonné">{{cite book |title=History of functional analysis |author=Jean Alexandre Dieudonné |url=https://books.google.com/books?id=mg7r4acKgq0C |isbn=0-444-86148-3 |year=1981 |publisher=Elsevier}}</ref> It is a result of studies of [[linear algebra]] and the solutions of [[System of linear equations|systems of linear equations]] and their generalizations.<ref name=Arveson>{{cite book |title=A short course on spectral theory |author=William Arveson |chapter=Chapter 1: spectral theory and Banach algebras |url =https://books.google.com/books?id=ARdehHGWV1QC |isbn=0-387-95300-0 |year=2002 |publisher=Springer}}</ref> The theory is connected to that of [[analytic functions]] because the spectral properties of an operator are related to analytic functions of the spectral parameter.<ref name="Sadovnichiĭ">{{cite book |title=Theory of Operators |author=Viktor Antonovich Sadovnichiĭ |chapter=Chapter 4: The geometry of Hilbert space: the spectral theory of operators |chapter-url=https://books.google.com/books?id=SR1QkG6OkVEC&pg=PA181 |page= 181 ''et seq'' |isbn=0-306-11028-8 |year=1991 |publisher=Springer}}
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