Definition
You define any transform in 2 dimensions with the vector
They have the properties that:
- They can be represented by a Matrix
A-Level Further Core 1
Reflections and Rotations
You can describe any linear transform just by the effect it has on unit vectors as every vector is a linear combination of the unit vectors.
Points/lines that don’t change under the transform are called invariant.
The matrix
Enlargement and Stretches
You can represent a stretch with matrix
Reflections
Rotations
Successive transformations
The matrix
Linear Transforms in 3D
For a linear transform by a given 3x3 Matrix
Inverting Transforms
Since