Index: Difference between revisions
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added index of a Fredholm operator (i.e., in the sense of "index theory'') |
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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 subgroup]] is the number of its left [[coset]]s (which is equal to the number of its right cosets). |
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The index of a [[Fredholm operator]] is the dimension of its [[kernel]] minus the dimension of its [[cokernel]]. |
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Revision as of 12:30, 27 July 2003
An index (plural. indices) is a pointer that takes you to information. Traditionally indexes (also pluralised particularly in Europe as indices) are found at the back of books. They complement the contents page because they give access to information by its specific name; contents pages, on the other hand, give access through broad categories. Indexes are usually organised alphabetically; contents pages are organised according to the order of pages in the book.
Indexing skills have also been applied to periodicals and databases, and web indexing is now becoming important.
In mathematics, an index (plural indices) 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 label a set or sequence of variables.
The index of a subgroup is the number of its left cosets (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.
In computer science, an index is usually used for expressing an nth element. Indices are usually expressed as integers.