Definition for "Spectrum" in the Quantum Dictionary

- Mathematics & Logic -

Pure Mathematics Dictionary

The set of scalars λ for which the operator shift T−λI fails to be invertible; it captures the total spectral properties of an operator, generalizing eigenvalues to infinite-dimensional and non-normal contexts.

- Pure Mathematics -

Algebra Dictionary

The set of scalars λ in the base field (typically C) for which the operator T−λI fails to be invertible in the ambient algebra/topology; for bounded operators on Banach spaces the spectrum splits into point, continuous and residual parts.