Linear Transformation of Unit Vectors

This example shows the linear transformation of unit vectors Vi (the x unit vector) and Vj (the y unit vector)

Two main things to note here:

  1. How changing the unit vectors warps the vector space; and
  2. that the value of Vc doesn't actually change.
0
1
-1
0
1.5
-1.5
=
0 × 0   +  
0 × 0   +  
0 × 0
0 × 0
=
1.5
-1.5