Diagonalne

Diagonalne is the Polish term derived from diagonalny, used as an adjective to describe things related to diagonals or running along a diagonal. In mathematical and technical contexts it appears in geometry, linear algebra, and related disciplines, as well as in everyday language when describing lines or directions angled from a reference axis.

In geometry, a diagonal is a line segment connecting two non-adjacent vertices of a polygon. In a rectangle or square, the diagonal joins opposite corners. The length of a rectangle’s diagonal is given by the square root of the sum of the squares of its sides. A polygon with n vertices has n(n−3)/2 diagonals, provided it is simple (non-self-intersecting). In three-dimensional figures, space diagonals connect opposite vertices that do not lie on the same face.

In linear algebra, diagonalne concepts include the diagonal matrix, which has nonzero entries only on the main diagonal and zeros elsewhere. A matrix is called diagonalizable if it can be transformed, via similarity, into a diagonal matrix. The diagonal entries of such a matrix are typically the eigenvalues of the original matrix.

Diagonals also appear in applied fields: in computer graphics for line clipping and rasterization, in architecture and design for structural and aesthetic purposes, and in graph theory where diagonals relate to connections beyond the edges of a polygonal shape.

The term is used across disciplines to denote orientation, measurement, or properties that align with or occur along a diagonal direction, contrasting with horizontal or vertical components.