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Spectrum (functional analysis)
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Spectrum (functional analysis)
In
mathematics
, particularly in
functional analysis
, the
spectrum
of a
bounded operator
is a generalisation of the set of
eigenvalues
of a
matrix
. Specifically, a
complex number
λ is said to be in the spectrum of a bounded linear operator
T
if λ
I
−
T
is not
invertible
, where
I
is the
identity operator
. The study of spectra and related properties is known as
spectral theory
, which has numerous applications, most notably the
mathematical formulation
of
quantum mechanics
.
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