Index (mathematics)

The word ''index'' is used in variety of senses in Mathematics .

In perhaps the most frequent sense, an index is a Superscript or Subscript 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 or Array or sequence of variables. See also '' Index Set '', '' Indexed Family '', and Index (information Technology) .

The Index Of A Subgroup is the number of its left Coset 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 its Cokernel .

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.

x^a \mapsto rac{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 the Poincaré–Hopf Theorem which relates the sum of the indices of a vector field to the Euler Characteristic of the manifold. The Hairy Ball Theorem is a special case. Confer Fixed 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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