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August 16[edit]

Name For Vectors Whose Components Sum To 1[edit]

In something I'm working on, I keep encountering the need for vectors (v_0,...v_n) where v_0 +...v_n = 1. I know a couple of other places these are used, but I've never seen them given an explicit name, is there one?24.3.131.165 (talk) 12:06, 16 August 2021 (UTC)[reply]

If the context is probability, these may be probability vectors (aka stochastic vectors). In other contexts the term "weights vector" can be found (not to be confused with the unrelated concept of "weight vector" from the representation of Lie algebras). In either case the elements are usually required to be nonnegative. I'm not aware of a context-independent name. You may encounter the term "normalized vector", but this name can be confusing unless the L¹ norm is implied by the context and the elements are nonnegative. --Lambiam 15:08, 16 August 2021 (UTC)[reply]

Probability/stochastic vectors also require each entry to be ≥0. They correspond to the Convex combinations of a given set of points. If you drop the ≥0 requirement in convex combinations then you get Affine combinations, but I don't know of a name for what you get when you vectorize the coordinates. The term Barycentric coordinates comes close, depending on context. But while they may be ordered tuples, that's not exactly the same as being a vector. You can talk about the point (1, 2), meaning the point with coordinates (1, 2) in a given coordinate system, and similarly the vector (1, 2). But a point is not the same a vector, and neither is an ordered tuple, despite their sometimes being identified in informal language. --RDBury (talk) 21:47, 16 August 2021 (UTC)[reply]

They seem to be sometimes called compositional data, a "composition", or a "compositional vector" [1]. This goes along with the additional requirement that the components be >= 0 (which you may or may not have also had in mind). --Amble (talk) 19:03, 17 August 2021 (UTC)[reply]