m1×n1

m1×n1 is a notation used to indicate a two-dimensional size or product of two dimensions, typically read as “m one by n one” or simply “m1 by n1.” It is commonly used in mathematics, computer science, and related fields to describe the size of a two-dimensional object such as a matrix, an array, an image, or a grid, where m1 and n1 are positive integers.

An object of this size has m1 rows and n1 columns and contains m1×n1 elements. The notation parallels the standard m×n convention in linear algebra, with an index to differentiate between different dimension pairs when multiple shapes are involved. In many contexts, m1 and n1 designate specific dimensions of interest, such as the dimensions of a particular matrix or two-dimensional array.

Applications include matrices in linear algebra, two-dimensional arrays in programming, digital images (height by width in pixels), and tiling or grid problems in combinatorics. For example, a 4×3 matrix has 12 entries, and a 5×7 grid contains 35 cells. In matrix algebra, the product AB has size m1×p when A is m1×n1 and B is n1×p, illustrating how inner dimensions must match for multiplication.

Notes: dimensions are generally assumed to be integers at least 0 in practical contexts; if either dimension is zero, the object has zero elements. While m1×n1 is a readable form for describing shape, standard practice in some texts uses the simple m×n notation when the indices are not needed for distinction.