A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. It is a fundamental tool in linear algebra and is used to represent and manipulate systems of linear equations.
Matrices are used in linear algebra to represent and solve systems of linear equations, perform transformations and rotations in geometry, and represent data in statistics and machine learning. They also have applications in fields such as physics, economics, and computer graphics.
The basic operations in matrix algebra include addition, subtraction, multiplication, and division. Matrices can also be transposed, scaled, and inverted.
Matrices are typically represented in computer programs as two-dimensional arrays. Each element in the array corresponds to a number or symbol in the matrix. Various programming languages have built-in functions and libraries for performing matrix operations.
A square matrix has an equal number of rows and columns, while a rectangular matrix has different numbers of rows and columns. Square matrices have special properties and are used in many applications, while rectangular matrices are more general and can represent a wider range of data.