Visualizing Eigenvectors
Author: Marc Renault

u = (2.487797011389929, 0.5971652433292804)
v = (1, 3)
Pts = Sequence((cos(2.0 * 3.142 k / 48.0), sin(2.0 * 3.142 k / 48.0)), k, 1.0, 48.0, 1.0)
Mat: {{x(u), x(v)}, {y(u), y(v)}}
MPts = Sequence(Mat Element[Pts, k], k, 1.0, Length[Pts], 1.0)
mvecs = Sequence(Vector[Vector[Element[Pts, k], Element[MPts, k]]], k, 1.0, Length[Pts], 1.0)
vecs = Sequence(Vector[Vector[Element[Pts, k]]], k, 1.0, Length[Pts], 1.0)
Mtext: "\left[
  \begin{array}{ c c }
    " + (x(u)) + " & " + (x(v)) + " \\
     " + (y(u)) + " & " + (y(v)) + "
  \end{array} \right] "
Dtext: "det = " + (Determinant[{{x(u), x(v)}, {y(u), y(v)}}])

Tool: Linear Transformation (command LinearTransformation)
Vector, Vector, Point
Input: B, C, D
Output: E

E: (x(B) x(D) + x(C) y(D), y(B) x(D) + y(C) y(D))