Diagonalny

Diagonalny is an adjective in Polish that denotes a relation to a diagonal, the line or direction connecting opposite corners of a figure. The term is borrowed from the concept of a diagonal and is used across technical fields, especially in mathematics and related disciplines. In Polish, the word has gendered forms: diagonalny (masc.), diagonalna (fem.), diagonalne (pl.).

In geometry, the standard Polish term for a line connecting non-adjacent vertices is przekątna. Nevertheless, diagonalny appears in contexts describing diagonal aspects of shapes or diagrams, such as a diagonal line (linia diagonalna) across a polygon or a grid. The main diagonal of a square or rectangle is commonly referred to as the główna przekątna; in some technical usages the diagonal properties may be described with diagonalny to emphasize diagonal orientation.

In linear algebra and related areas, the phrase macierz diagonalna denotes a matrix with nonzero elements only on its main diagonal. Diagonalny is often used to describe properties or operations associated with diagonality, such as diagonalization (diagonalizacja) — the process of transforming a matrix into a diagonal form via a suitable basis. Related terms include diagonalizowalny (diagonalisable) and diagonalny układ.

Beyond pure mathematics, diagonalny appears in design, graphics, and technical descriptions to convey a diagonal orientation or pattern. The word smoothly adapts to plural and feminine forms as needed: diagonalne, diagonalna.