a matrix can change the direction a vector is pointing.
However, some vectors don't get their directions changed, but instead are scaled.
It was described that those vectors are eigen vectors and because every other vector is moving, and the eigen vector isn't, the eigenvector can be seen as the axis of rotation for the matrix.
The visual representation of what the matrix is doing, "rotating around the eigen vector" is shown literally. However, I know for a fact matrices can have multiple eigenvectors, but how can something have multiple axis of rotations?