A matrix is essentially a rectangular array of numbers, symbols, or expressions arranged in rows and columns.

This is a 3x3 matrix, meaning it has 3 rows and 3 columns respectively:

Matrix Indexing

Each element can be identified by its row and column. For example, the element 6 is located at the index .

Matrix Usage

Matrices are used to represent a wide variety of things in mathematics, such as:

Systems of Linear Equations
Transformations of points in space
Data sets
Statistical relationships

Matrix Operations

Here are some of the basic operations that can be performed on matrices:

Addition: Matrices can be added if they have the same dimensions. Simply add the elements component-wise.
Subtraction: Matrices can be subtracted if they have the same dimensions. Simply subtract the elements component-wise.
Multiplication: Matrices can be multiplied with a scalar by multiply each element of the matrix by the scalar.
When two matrices are multiplied together it is called the Dot Product
Determinants