# Index

(Redirected from Index (mathematics))
For the use of the word "index" in Wikipedia, see Wikipedia:Index (disambiguation)

An index is an indirect shortcut derived from and pointing into, a greater volume of values, data, information or knowledge. Index may refer to:

• Index (retailer), a defunct UK catalogue retailer formerly owned by the Littlewoods group and known as Littlewoods Index
• Index Corporation, a Japanese video game developer
• INDEX, a market research fair in Lucknow, India
• Index fund, a collective investment scheme
• Stock market index, a statistical average of prices of securities

## Sciences

### Biological sciences

• Diversity index – a quantitative measure that increases when the number of types into which a set of entities has been classified increases, and obtains its maximum value for a given number of types when all types are represented by the same number of entities

### Economics

• Index (economics), a single number calculated from an array of prices and quantities
• Price index, a typical price for some good or service

### Linguistics

• Indexicality, the variation of meaning of an utterance according to certain features of the context in which it is uttered

### Mathematics

• A number or other symbol that indicates the location of a variable in an indexed family or set such as a list or array of numbers or other mathematical objects, usually written as a subscript to the variable; e.g. in the list $\lbrace x_1, x_2, x_3, x_4\rbrace$, the number $3$ is the index of the third element, $x_3$.
• A numerical value attached to a mathematical object, such as those listed here under Algebra and Analysis
• The index of summation i is used to calculate a sum, e.g.:
$\sum_{i \mathop =3}^5 i = 3+4+5 = 12.$

#### Algebra

• The degree of an nth root
• The index of a subgroup is the number of a subgroup's left cosets (which is equal to the number of its right cosets).
• The index of a linear map, is the dimension of the map's kernel minus the dimension of its cokernel.
• The index of a real quadratic form Q is defined (but not always consistently) as pq where Q can be written as a difference of p squared linear terms and q squared linear terms.
• The index of a matrix is the least integer k ≥ 0 such that rank(Ak+1) = rank(Ak).

#### Analysis

• The winding number of an oriented closed curve on a surface relative to a point on that surface; loosely speaking, the number of times the curve goes around the point counter-clockwise
• The index of a vector field v at an isolated zero is the degree of the map $x^a \mapsto \frac{v^a(x)}{\sqrt{\sum_b(v^b(x))^2}}$, taking points near the zero into the unit sphere.

## Technologies

### Mechanics

• Indexing (motion), a kind of motion in many areas of mechanical engineering and machining