Eigenvector Visualizer

The source default matrix has rows two one and one two. Multiplying vector one one gives three three, so this line has eigenvalue three. Multiplying one minus one gives one minus one, so that line has eigenvalue one. The animated arrow grows threefold along the same direction. A general vector can mix these two directions and change direction after transformation. The source singular preset is rows one two and two four. Its determinant is zero and trace five, yielding eigenvalues five and zero. Vector one two stretches to five ten; vector minus two one becomes zero zero. Area collapses because an independent direction is lost. The bars compare the scale factors, while the fading-length arrow shows the null direction collapsing. The rotation preset uses zero point eight seven and zero point five, rather than exact cosine thirty degrees. Its determinant is zero point eight seven squared plus zero point five squared, or one point zero zero six nine. Column length is square root of that, about one point zero zero three four four. Thus this source fixture slightly expands lengths and areas. Its negative characteristic discriminant means no real invariant direction for this transformation. The preset label alone should not be treated as an exact unit rotation.