What is matrix definition?

A matrix is a rectangular array or table of numbers or variables, arranged in rows and columns. It is a mathematical concept that is used to represent a set of equations or to perform operations like addition, subtraction, multiplication, and division. Matrices are often used to solve systems of linear equations, and are an essential tool in modern mathematics and sciences.

The size of a matrix is denoted by the number of rows and columns it contains. For example, a matrix with 3 rows and 2 columns is called a 3x2 matrix. Matrices can also be classified based on the type of elements they contain, such as real numbers, complex numbers, or even other matrices.

Matrices can be represented in different ways, including by listing their elements in brackets, using variables to represent the elements, or by using a graphical representation known as a matrix diagram.

In addition to the basic operations of addition, subtraction, multiplication, and division, matrices can be transposed (flipped along the diagonal), inverted (multiplied by another matrix to give the identity matrix), and multiplied by scalars (numbers). Matrices are essential in fields such as computer graphics, physics, engineering, and economics.