Linear Algebra

Dynamical Problem Sheet 4: Basic Linear Transforms in R²

projection,
reflection,
dilation and
rotation,

Naturally, the plane is equipped with the standard vector space operations, the coordinate-wise vector addition and multiplication by scalars.

Using the mouse you can drag the variable u and control the transformations in appropriate ways. Feel free to explore!

I Basic Transformations: Projection, Reflection, Dilation and Rotation

I 1 Projection (on horizontal axis)

I 2 Reflection (over horizontal axis)

I 3 Dilation by scalar c (from x₁-axis)

I 4 Dilation by scalar c (from the origin)

I 5 Rotation (by angle a)

6 Translation by a constant vector a (is not linear!)