The Hidden Maths Behind Everything You See

A matrix is a rectangular arrangement of numbers, symbols, or expressions organised into rows and columns.

The word 'matrix' comes from the Latin word for 'womb' or 'source', suggesting something that contains or generates other things.

Matrices are a fundamental tool in mathematics, used across many different fields of study and industry.

Each number inside a matrix is called an element, and its position is described by its row and column number.

A matrix with the same number of rows and columns is called a square matrix, which has special mathematical properties.

Mathematicians can add two matrices together by simply adding the elements that share the same position.

Multiplying matrices is more complex and follows a specific set of rules that must be applied carefully.

Matrices are used in computer graphics to rotate, scale, and move images on a screen.

Engineers use matrices to solve systems of equations that would be extremely difficult to work out by hand.

In economics, matrices help analysts model how changes in one sector can affect the rest of an economy.

Physicists use matrices to describe the behaviour of particles at the quantum level, where ordinary logic often breaks down.

Machine learning and artificial intelligence rely heavily on matrix calculations to process large amounts of data efficiently.

A matrix can be transformed using operations such as transposition, which means swapping its rows and columns.

The determinant is a special number calculated from a square matrix and tells mathematicians important information about it.

Understanding matrices opens the door to some of the most powerful and widely used ideas in modern science and technology.