n. a subset of Euclidean n-space (Euclidean space) that is closed under addition and subtraction; most usually, such a set constructed as all integral combinations of n linearly independent points or generators. The celebrated Minkowski theorem asserts that any symmetric convex body of volume greater than 2ⁿd(Λ) contains a non-zero member of the lattice Λ, where d(Λ) is the determinant of the matrix of which the rows are the coefficients of the generators.