jIndizes

jIndizes is a convention used to label coordinates along the second dimension of a multi-dimensional data structure. The term appears in contexts where elements are addressed by index pairs or tuples such as (i, j), with i typically referring to the first dimension and j to the second. The concept is common in mathematics, computer science, and data processing and is often discussed in materials on multi-index notation.

Notation and meaning

In a two-dimensional array A, the element A[i, j] is identified by an iIndex and a jIndex. In higher-order arrays, a jIndex may denote the coordinate in the second mode or column-like dimension, while iIndices denote the first mode or row-like dimension. Distinguishing iIndizes and jIndizes helps to clarify algorithms that sweep across one dimension while holding the other fixed. This separation also underpins how people describe substructures such as submatrices or slices.

Contexts and applications

jIndizes are used in linear algebra to refer to columns within a matrix, and in tensor calculus to label the second factor of a product. In sparse matrix formats, such as coordinate (COO) or compressed sparse row/column formats, pairs of indices (i, j) serve as coordinates for nonzero elements, with the jIndex indicating the column coordinate. In programming, inner loops often iterate over jIndizes to traverse columns, while outer loops advance over iIndizes to move across rows.

Implementation considerations

In software, jIndizes may be stored as separate arrays of integers (e.g., a parallel array of j values) or interleaved with iIndizes. Choices affect memory locality and performance, particularly for large, multi-dimensional datasets. Indexing conventions can also differ between 0-based and 1-based systems.

See also

Multi-index notation, row and column indices, tensor mode indices, sparse matrix formats.