Covectors

Part of speech: noun

Definitions

1. A mathematical object that maps vectors to scalars, usually functioning as linear functionals in the context of linear algebra
2. An entity in vector spaces representing dual elements that act on vectors to produce real numbers, often used in physics and engineering
3. A type of linear transformation associated with a vector space that provides a means of evaluating vectors through a scalar output

Etymology: "Covectors" is the plural of "covector," a compound formed from the prefix "co-" and "vector." The "co-" here is the same prefix found in words like "cofactor" and "coordinate," and it carries the sense of "with" or "together," signalling a partner or counterpart to the original term. In this case, a covector is the mathematical counterpart to a vector: where a vector is an arrow-like quantity, a covector is an object that takes a vector as input and returns a number. The word belongs to the modern technical vocabulary of linear algebra and differential geometry, built from the familiar parts rather than inherited from older language. Its pairing with "vector" shows how mathematicians name the dual of an object by attaching a prefix to the original term, so the relationship between the two concepts is written directly into the word.

Synonyms: dual vectors