matrikksen

Matriksen is the definite form of the noun matriks in Norwegian and Danish, used to denote the mathematical object known in English as the matrix: a rectangular array of numbers, symbols, or expressions arranged in rows and columns. The term derives from the Latin matrix, via French matrice, and was adopted into Scandinavian languages to describe this formal concept.

In mathematics, a matriks serves as a compact representation of linear transformations with respect to a given basis. It enables the computation of outputs for given inputs through matrix multiplication. Common operations on a matriks include transposition, multiplication with other matrices, and, when the matrix is square and invertible, finding its inverse. Determinant and rank are key properties that help determine invertibility and the solution structure of related linear systems. Matriksen can have real or complex entries and can be defined over more general fields in abstract linear algebra.

In applied contexts, matriksen is used to model and solve practical problems. In computer graphics, matrices represent transformations such as rotation, scaling, and translation. In statistics and data analysis, data are organized into matrices to perform operations like regression, covariance calculation, and principal component analysis. Adjacency matrices and incidence matrices in graph theory are specific examples where a matriks encodes relationships between entities.

Common special cases include the identity matrix, diagonal matrices, and symmetric or diagonalizable matrices, each with particular properties that simplify computations. In education and formal writing, standard notation places the matriks elements inside brackets or parentheses, with dimensions indicated as m×n for a matrix with m rows and n columns. See also matrix (mathematics).