SumVi

SumVi is a shorthand notation used in some mathematical and computational texts to denote the sum of values indexed by a specified index set V_i. It is not part of the standard formal summation notation, but rather an informal convention that helps describe index-based aggregations without writing explicit sigma notation. In its simplest form, let I be a finite index set and v: I -> R a function assigning a value to each index. The expression sumVi v(i) denotes the sum of v(i) as i ranges over I. If the index domain is a subset J of I, then sumVi v(i) over i in J specifies the sum of v(i) for i in J.

The concept can be extended to weighted sums by including a weight function w: I -> R. In that case, sumVi w(i) v(i) represents the sum of the products w(i)·v(i) for all i in the chosen index set. This notation is commonly used in quick proofs, algorithm descriptions, and data-analytic notes where the index set is important but writing full sigma notation would be cumbersome. It is important to define the index set explicitly when using sumVi to avoid ambiguity, especially in programming contexts where the same symbol might be used differently.

Examples help clarify the idea. If v has components v1, v2, v3 with i in {1,2,3}, then sumVi v(i) equals v1 + v2 + v3. If weights w1, w2, w3 are given, sumVi w(i) v(i) equals w1·v1 + w2·v2 + w3·v3.

See also: Summation notation, dot product, aggregation, map-reduce.