Shears & Eigenvectors

Drag q'₂ horizontally to create a horizontal shear, or drag q'₁ vertically to create a vertical shear. Notice which axis remains invariant!

Invariant Axis Found

The eigenvector is q₁ (the x-axis).

HORIZONTAL SHEAR

The unit vectors transform as:

q₁ =
1 0
q'₁ =
1.0 0.0
q₂ =
0 1
q'₂ =
0.5 1.0
⇒ The Matrix A =
1.0 0.5
0.0 1.0

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Linear Algebra for Computer Science

Grid: 0.5 units / line
Unit Square
Transformed Space
Column 1 (q'₁)
Column 2 (q'₂)