- Index (mathematics)
The word

**"index**" is used in variety of senses inmathematics .* In perhaps the most frequent sense, an

**index**is asuperscript orsubscript to a symbol. Superscript indices are often, but not always, used to indicate powers. Subscript indices are usually used to identify an element of a set orarray or sequence of variables. See also "index set ", "indexed family", andIndex (information technology) .* Index meaning

exponent , the power to which some base is raised. See also 'Indices Laws '/'Laws of Indices '/'Laws of Exponents '.* The

index of a subgroup is the number of its leftcoset s (which is equal to the number of its right cosets).* The index of a

Fredholm operator is the dimension of its kernel minus the dimension of itscokernel .* The index of a real

quadratic form "Q" is defined (but not always consistently) as "p" − "q" where "Q" can be written as a difference of "p" squared linear terms and "q" squared linear terms.* 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 . This index is used in the statement of thePoincaré–Hopf theorem which relates the sum of the indices of a vector field to theEuler characteristic of the manifold. Thehairy ball theorem is a special case. Conferfixed point index .* "An index relates the value of a variable (or group of variables) to a base level, which is often the value on a particular date. The base level is set so that the index produces numbers that are easy to understand and compare. Indices are used to report on a wide variety of variables, including prices and wages, ultraviolet levels in sunlight, and even the readability of textbooks." from Mathematics of Data Management published by McGraw-Hill Ryerson

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