Rivijärjestys

Rivijärjestys is a Finnish term used to describe the arrangement or ordering of the rows of a matrix, table, or other two-dimensional data structure. It refers to a specific permutation of row indices or to the rule by which rows are sorted or reorganized. The concept is used across mathematics, data management, and computing to describe how rows are arranged for analysis, presentation, or processing.

In mathematics, rivijärjestys arises when the order of rows is changed during procedures such as Gaussian elimination. Swapping rows, or otherwise permuting them, is performed to place a suitable pivot and improve numerical stability. The resulting sequence of rows constitutes the rivijärjestys of the matrix at that stage. Row order may affect the behavior of algorithms, particularly in solving systems of linear equations or evaluating determinants.

In data management and databases, rivijärjestys describes how rows are ordered within a data set or relational table, usually according to the values in one or more key columns. Sorting operations produce a defined rivijärjestys, which can influence query results, indexing efficiency, and performance.

In computing, the concept is relevant to memory layout and data processing. The order of rows can impact cache locality and access patterns, especially when working with large matrices or data frames. Some programming libraries make row order explicit when transforming, sorting, or filtering two-dimensional data.

Example: A 3×2 matrix has rows r1, r2, r3 with first-column values 3, 1, 2. Sorting ascending yields the rivijärjestys [2, 3, 1].