n×mmatriisien

An n×m matrix, also known as a rectangular matrix, is a mathematical structure consisting of n rows and m columns of numbers, symbols, or expressions. Each element within the matrix is identified by its row and column indices. Matrices are fundamental in linear algebra and are widely used in various fields such as physics, engineering, computer science, and economics.

The dimensions of an n×m matrix are given by the number of rows (n) and the number of columns (m). For example, a 2×3 matrix has two rows and three columns. Matrices can be represented using various notations, with the most common being square brackets or parentheses enclosing the elements.

Matrices can be manipulated through various operations, including addition, subtraction, and multiplication. Matrix multiplication, in particular, is a key operation that allows for the combination of matrices to produce new matrices. The product of an n×m matrix and an m×p matrix results in an n×p matrix, provided that the number of columns in the first matrix equals the number of rows in the second matrix.

Matrices are also used to represent systems of linear equations, transformations in geometry, and data structures in computer science. The study of matrices and their properties is a cornerstone of linear algebra, providing a powerful toolkit for solving complex mathematical problems.