Eigen Explorer
Most directions come out of a matrix bent. A few come out only stretched — turn v until you find them.
Tip: park v at 0° on Stretch, read the stretch, then take on the Mirror.
Try this
- Bag the easy pair. On Stretch, park v at 0° (stretch 2) and 90° (stretch 0.5): the axes are the answer.
- Find the flip. On Mirror, hunt both surviving lines — one stretches by 1, the other by −1. The minus is a direction flip, not a shrink.
- Prove the negative. On Turn 90°, drag v through the full half-circle and confirm nothing ever aligns — then reveal to certify the emptiness.
How to read the hunt
An eigenvector is a direction the matrix cannot turn: Av lands on the same line as v, only scaled — or flipped, when the eigenvalue is negative. The alignment readout scores this: 1.000 means on the line, anything less means bent.
Some matrices have two surviving lines, some one, some none: a 90° rotation turns every arrow, so there is honestly nothing to reveal. Watch the stretch column when you land on a line — that number is the eigenvalue.
Linear algebra is geometry in disguise
Eigenvectors unlock vibrations, search rankings, and quantum states — ManySpace teaches the whole subject the way you just hunted this one: by turning things until they click.