Doubleindexed

Doubleindexed (hyphenated as double-indexed) is a descriptive term used to refer to objects that are accessed or organized by two indices. It is commonly applied in mathematics, computer science, and related fields to describe data structures, equations, and components that depend on a pair of indices rather than a single one.

In mathematics, a double-indexed object typically consists of a family of elements aij indexed by two indices i and j. A classic example is a two-dimensional array or matrix, whose entries form a second-order tensor with components Tij. Notation such as aij or Tij is standard, and operations may involve double sums like ∑i ∑j f(i, j) or the tensor contraction over one or both indices.

In computing, double indexing is synonymous with two-dimensional arrays or matrices. These are stored as contiguous blocks and accessed via two indices, for example A[i][j] in languages like C or Python, or A(i, j) in languages such as Fortran. Performance considerations often center on memory layout (row-major vs column-major) and access patterns to optimize cache efficiency.

Double indexing also appears in statistics and data analysis, where data are organized across two dimensions, such as individuals and time periods (panel data). In such contexts, the two indices enable analyses that track changes over one dimension while holding the other constant.

Related concepts include matrices, two-dimensional arrays, and higher-dimensional tensors, which generalize the idea of indexing with two or more dimensions. Doubleindexed objects provide a straightforward framework for representing and manipulating data with paired indices.