Indices

Indices, or indices, are indicators used to express the value, position, or ranking of elements within a system. The term originates from Latin indicare, meaning to point out or indicate. Indices appear across many disciplines, sometimes with related but distinct meanings.

In mathematics and related fields, an index labels the position of an element in a sequence, array, or structure. For example, a_i denotes the i-th term of a sequence, while a_{ij} can index a matrix entry. Indices enable compact notation for sums, products, and tensors, including multi-index notation used in higher dimensions.

In computing and information systems, indexing refers to organized data structures designed to speed up retrieval. A database index accelerates queries by providing quick access to rows, often implemented as B-trees or hash-based structures. In information retrieval, inverted indexes map terms to documents containing them, enabling efficient full-text search.

In publishing and reference works, an index is an ordered list of topics, names, or concepts with page references, helping readers locate information within a book or across a corpus.

In economics and finance, market or economic indices aggregate the performance or value of a group of assets or indicators to reflect broader trends. Common examples include stock market indices (such as those tracking a wide market or a sector) and price indices like the consumer price index, which measure changes in price levels over time.

Overall, indices serve as tools to locate, summarize, or compare information within complex systems, across mathematics, computer science, publishing, and economics.