vectorv
Vectorv is a term used in some mathematical discussions to denote an augmented vector, defined as an ordered pair (v, a) where v is a conventional vector in R^n and a is a scalar in R. The collection of all vectorvs is the Cartesian product R^n × R, which is itself a real vector space of dimension n+1 and is isomorphic to R^{n+1}.
Operations on vectorvs are performed componentwise: (v1,a1) + (v2,a2) = (v1+v2, a1+a2) and α·(v,a) = (α v, α a) for scalar
In practice, vectorv can be used to encode both position and a scalar attribute, such as intensity,
Variants include choosing different base fields (e.g., C^n or finite fields) or different coupling in the inner
See also: augmented vector, product space, feature vector, multivariate data.