Spectrum of an operator

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The spectrum of an operator is the set of scalar values for which the operator minus that scalar times the identity does not have a bounded inverse. It generalises the collection of eigenvalues familiar from finite-dimensional matrices.

In finite-dimensional linear algebra, the spectrum consists exactly of the eigenvalues. In infinite-dimensional spaces, it may also include values that are not associated with ordinary eigenvectors.

The spectrum can be divided into point, continuous, and residual parts, depending on the behaviour of the operator and its range. For self-adjoint operators, the spectrum is real.

Operator spectra are fundamental in functional analysis, differential equations, quantum mechanics, vibration theory, stability analysis, and the study of waves and resonances.

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• Source / publisher: Wikipedia
• URL type: WWW
• Credits: Wikipedia
• URL: https://en.wikipedia.org/wiki/Spectrum_of_an_operator