A linear transformation is a geometric transformation made of a combination of any or all of:
- rotations centred on the origin
- reflections about lines through the origin
- scalings centred on the origin (for example, a stretch in the \(x\)-direction).
Enlargements and shears are examples of linear transformations, as they can be produced by a combination of the above basic types.
Linear transformations can be represented using matrices. Each linear transformation corresponds to a matrix, and the image of each point is obtained by multiplying this matrix by the position vector of the point. For example, in 2 dimensions, a rotation of \(90^\circ\) corresponds to the matrix \(\bigl(\begin{smallmatrix}0&-1\\1&0\end{smallmatrix}\bigr)\).
