Matrix Mixing & Eigenvectors
A symmetric matrix M mixes the x and y directions — until you find its natural axes.
Unit circle
Transformed ellipse
Where axes land (mixed)
Eigenvectors (unmixed)
x-scale
a
=
2.0
y-scale
d
=
1.5
mixing
b
=
1.0
M =
2.0
1.0
1.0
1.5