determinanttien

Determinanttien is the Finnish genitive plural form of determinantti, the word for "determinant" in mathematics. In Finnish grammar it denotes possession, relation or qualification involving more than one determinant and is commonly used in mathematical texts and discussions (for example, determinanttien ominaisuudet = "properties of the determinants").

As a mathematical concept, a determinant is a scalar value associated with a square matrix that encodes information about invertibility, volume scaling, and linear dependence. Key properties often invoked in contexts where the term determinanttien appears include multilinearity in rows or columns, antisymmetry (sign change on row swaps), det(AB) = det(A) det(B), and det(A) = 0 characterizing singular (non-invertible) matrices. Determinanttien laskeminen (calculation of determinants) uses methods such as expansion by minors, row-reduction, or applying specific formulas for small matrices.

Morphologically, determinantti follows regular Finnish declension patterns: singular nominative determinantti, genitive singular determinantin, plural nominative determinantit, and genitive plural determinanttien. The form is used in compound phrases and technical expressions (e.g., determinanttien arvot, determinanttien erotus). It appears primarily in formal written Finnish within linear algebra, differential equations, numerical analysis and related fields.

Related terms include determinantti (nom.), determinantin (gen. sing.), and determinantit (nom. pl.).