m×k

m×k (read “m by k” or “m times k”) is a conventional way to denote either the product of two integers or the dimensions of a rectangle or grid with m units along one side and k units along the other. The symbols are used across mathematics and applied disciplines, with m and k typically being nonnegative integers.

In linear algebra, an m×k matrix has m rows and k columns. The transpose of an m×k matrix is a k×m matrix. A matrix is square when m = k, in which case concepts such as determinant and inverse are defined under appropriate conditions. The product of two matrices is governed by compatible inner dimensions, and the resulting matrix has dimensions determined by this rule.

In combinatorics, the Cartesian product of a set A with cardinality m and a set B with cardinality k has size m×k. More generally, if A and B are finite sets, their product A×B consists of m×k ordered pairs.

In geometry, m×k describes the dimensions of a rectangle or grid. In computer science and data organization, an m×k array or matrix stores data in m rows and k columns, affecting indexing, memory layout, and performance.

Notes: m and k are typically positive integers when referring to finite structures; when used as a product m×k, it denotes multiplication. The term is also encountered as “m-by-k,” especially in contexts such as matrices, grids, and dimensions. See also matrix, determinant, transpose, Cartesian product.