Chapter 10: Coordinate Transformations
Multiplying a matrix by a vector allows us to produce a new, changed vectors.
Such a transformation can be used to scale, shear, and rotate a vector or Cartesian coordinates.
There is a requisite diagram for understanding this which is coming soon…
is rotated by
makes angle with the x-axis and its length is
Using trigonometric relationships:
Substituting the equations for and :
And the transformation matrix is revealed.