Eigenvectors represent fixed directions, not fixed magnitudes. From Wikipedia:
> More precisely, an eigenvector v of a linear transformation T is scaled by a constant factor lambda when the linear transformation is applied to it: Tv = lambda v .
In other words, repeated multiplication of an eigenvector by a matrix can still create exponential growth.
> More precisely, an eigenvector v of a linear transformation T is scaled by a constant factor lambda when the linear transformation is applied to it: Tv = lambda v .
In other words, repeated multiplication of an eigenvector by a matrix can still create exponential growth.