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Spectral theory
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
s in a variety of
mathematical spaces
. It is a result of studies of
linear algebra
and the solutions of
systems of linear equations
and their generalizations. 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.
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