Eigen

stretch the sheet. find the lines that don't turn.

drag the probe across the stretching sheet to find the few pins that only slide straight out

Apply a matrix to a sheet and nearly every arrow is knocked off its line. A few aren't: they stay on their own line, only longer, shorter, or flipped -- the eigenvectors, scaled by the eigenvalue. A turn keeps none.

Concepts: linear-algebra, geometry, scaling.

An interactive you play with one thumb, on Wundr.