spectrum

Noun

spectrum (plural spectra or spectrums)

1. A range; a continuous, infinite, one-dimensional set, possibly bounded by extremes.
   • Near-synonyms: sliding scale, continuum
   • As Mr. Obama prepared to take the oath, his approval rating touched a remarkable 70 percent in some polling — a reflection of good will across the political spectrum.2012 November 7, Matt Bai, “Winning a Second Term, Obama Will Confront Familiar Headwinds”, in New York Times

   Synonyms:

   sliding scale, continuum

2. Specifically, a range of colours representing light (electromagnetic radiation) of contiguous frequencies; hence electromagnetic spectrum, visible spectrum, ultraviolet spectrum, etc.
   • Current 3G technologies can send roughly 1 bit of data - a one or a zero - per second over each 1 Hz of spectrum that the operator owns.2010 October 30, Jim Giles, “Jammed!”, in New Scientist
3. (usually) The autism spectrum.
   • He punctuated his words with a look into my eyes that might have been read as threatening or menacing by anyone who was not on the spectrum. But I am on the spectrum, and so I stared back at him.2022, Percival Everett, Dr. No, Influx Press (2023), page 110
4. A set of frequencies that are used for radio-frequency communication; not necessarily a continuous range.
5. The pattern of absorption or emission of radiation produced by a substance when subjected to energy (radiation, heat, electricity, etc.).
6. The set of eigenvalues of a matrix.

   Synonyms:

   eigenspectrum

7. (functional analysis) Of a bounded linear operator A, the set of scalar values λ such that the operator A—λI, where I denotes the identity operator, does not have a bounded inverse; intended as a generalisation of the linear algebra sense.
8. (commutative algebra) An abstract object in mathematics created from a commutative ring R and denoted operatorname Spec(R) or operatorname SpecR and said to be the spectrum of R; useful in the study of such rings for providing a geometric object which encodes many of the properties R, and in modern geometry for generalizing the notion of an algebraic variety to that of an affine scheme. Formally, the set of all prime ideals R equipped with the Zariski topology and augmented with a sheaf of rings called the structure sheaf, generated by the B-sheaf on the distinguished open sets D_f which assigns the localization of R at f to each set D_f, regarded as a ring of functions on D_f. See Spectrum of a ring on Wikipedia.Wikipedia
9. (obsolete) Specter, apparition.
10. The image of something seen that persists after the eyes are closed.