M×N

M×N is a mathematical notation used to denote either a product of two objects or the dimensions of a two-dimensional array, depending on context.

In matrix theory, an M×N matrix has M rows and N columns. Its entries are typically denoted aij, with 1 ≤ i ≤ M and 1 ≤ j ≤ N. The matrix contains M×N elements. In linear algebra and applications, the size M×N describes the shape of a matrix or a two-dimensional data array, such as an image with M by N pixels.

In set theory and combinatorics, M×N denotes the Cartesian product of sets M and N: the set of all ordered pairs (m,n) with m∈M and n∈N. If M and N are finite, the cardinality of M×N is |M|×|N|. The Cartesian product concept generalizes to more factors as well.

In arithmetic, M×N is the product of the numbers M and N, yielding a single number.

In computer science, geometry, and related fields, M×N grids appear in layouts, matrices, images, and discretized spaces such as pixel grids, tile maps, seating plans, and numerical simulations.

Notes: For matrices, the order matters; the transpose switches dimensions from M×N to N×M. For Cartesian products, M×N and N×M are distinct as sets but are often isomorphic via a simple coordinate swap, particularly when M and N are finite or structured sets.