Spectral

Spectral is an adjective derived from spectrum, used across disciplines to denote relation to spectra, frequencies, or eigenstructures.

In physics and chemistry, spectral refers to the spectrum of electromagnetic radiation or the components of a signal as a function of wavelength or frequency. Spectroscopy analyzes how matter absorbs, emits, or scatters light, revealing spectral lines unique to elements and compounds.

In astronomy, spectral analysis classifies stars by their spectra (O, B, A, F, G, K, M) and measures properties such as composition, temperature, and motion via redshift or blueshift of spectral lines; the spectral energy distribution describes the overall energy output across wavelengths.

In mathematics, the spectrum of an operator comprises values for which the operator fails to be invertible; the eigenvalues form part of the spectrum. Spectral theory studies these properties and underpins the spectral theorem, enabling decomposition of operators into simpler components. The term also appears in spectral radius and spectral norm as measures of operator size.

In computer science and data analysis, spectral methods use eigenvalues and eigenvectors of matrices derived from data, notably in spectral clustering, where the Laplacian's spectrum informs cluster structure; related techniques include spectral graph theory and Laplacian eigenmaps. In signal processing, power spectral density describes a signal's distribution of power over frequency.

The word is used in various specialized fields, but always refers to some form of spectrum, whether physical, numerical, or conceptual.