Diagonalna

Diagonalna is a feminine Polish adjective derived from diagonal, used in mathematical terminology to describe objects related to diagonals. The term appears most commonly in geometry and linear algebra, where it helps name specific structures and properties.

In geometry, a diagonal is a line segment that connects two non-adjacent vertices of a polygon. For a convex polygon with n vertices, the number of diagonals is n(n-3)/2. Diagonals may lie inside the polygon and can intersect one another, depending on the shape. In three-dimensional shapes, the term can also describe diagonals of faces or space diagonals that connect non-adjacent vertices of a polyhedron.

In linear algebra, the phrase macierz diagonalna (diagonal matrix) is used to describe a square matrix in which all off-diagonal entries are zero. The diagonal elements are the only potentially nonzero entries, located on the main diagonal. Diagonal matrices have several convenient properties: the product, sum, and power of diagonal matrices are easy to compute; the determinant equals the product of the diagonal entries; the trace equals the sum of diagonal entries; a diagonal matrix is invertible if and only if all diagonal entries are nonzero, with its inverse also diagonal. The eigenvalues of a diagonal matrix are exactly its diagonal elements.

The adjective diagonalna also appears in contexts such as “linia diagonalna” (a diagonal line) or in discussions of the main diagonal (główna przekątna) of a matrix. The term is widely used across mathematics to denote dihedral or diagonal features succinctly.