m×nmatriiseja

An m×n matrix, also known as a rectangular matrix, is a mathematical structure consisting of m rows and n columns of numbers, symbols, or expressions. The size of the matrix is defined by the number of rows and columns, denoted as m×n. Matrices are fundamental in linear algebra and are used to represent systems of linear equations, transformations, and data sets.

Matrices can be represented using various notations. One common notation is to enclose the elements in square brackets or parentheses, with each row separated by a new line. For example, a 2×3 matrix A can be written as:

A = [a11 a12 a13

a21 a22 a23]

where aij represents the element in the ith row and jth column.

Matrices can be added, subtracted, and multiplied, provided that their dimensions are compatible. The product of an m×p matrix and a p×n matrix results in an m×n matrix. Matrix multiplication is not commutative, meaning that AB is not necessarily equal to BA.

Matrices have numerous applications in various fields, including computer graphics, engineering, economics, and machine learning. They are used to solve systems of linear equations, perform transformations, and analyze data. The study of matrices and their properties is a crucial aspect of linear algebra and has wide-ranging implications in mathematics and its applications.