m×nmatrices

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. An m×n matrix is a matrix with m rows and n columns. The notation m×n is read as "m by n" and indicates the dimensions or order of the matrix. For example, a 2×3 matrix has 2 rows and 3 columns.

The elements of a matrix are the individual entries within the array. If an element is in the i-th row and j-th column of a matrix A, it is often denoted as a_ij. The number of elements in an m×n matrix is the product of its dimensions, m × n.

Matrices are fundamental in many areas of mathematics, science, and engineering. They are used to represent systems of linear equations, transformations in geometry, and data sets. Operations such as matrix addition, subtraction, scalar multiplication, and matrix multiplication are defined for matrices, with specific rules depending on their dimensions. For instance, matrix addition and subtraction can only be performed on matrices of the same dimensions, while matrix multiplication has more complex dimension requirements. The concept of an m×n matrix provides a general framework for understanding and manipulating these mathematical objects.