N×K

n×k is a mathematical notation representing the product of two integers, commonly denoted as n times k. In arithmetic, n×k equals the multiplication of n and k, and the operation is commutative, so n×k = k×n. The result is an integer when n and k are integers.

In geometry and combinatorics, n and k are often used as dimensions of a rectangular object. An n×k rectangle has n rows and k columns, and the total number of unit cells or entries in such a rectangle is n×k. This usage extends to arrays and matrices, where an n×k matrix has n rows and k columns. The total number of entries in the matrix is also n×k.

In the context of set theory, if A and B are finite sets with cardinalities |A| = n and |B| = k, the Cartesian product A×B has cardinality |A×B| = n×k, consisting of all ordered pairs (a, b) with a ∈ A and b ∈ B.

Examples and edge cases help illustrate the concept. For instance, 3×4 = 12, and 5×0 = 0. A matrix with either zero rows or zero columns is considered to have zero entries, a degenerate case of the n×k form. The notation is widely used in mathematics, computer science, and related disciplines to denote size, capacity, or the number of elements in a rectangular structure.