alt Hacker NewsTheir point was that "familiarity" apparently means different things for different people :P Someone using linalg in computer graphics applications may say they're familiar with it even though they've never heard the term "eigenvector". I'm not actually sure about what you mean – how does repeated multiplication reveal eigenvectors?
Consider a diagonalizable matrix A. For example, a real symmetric matrix. Start with any vector b and keep multiplying it with A.
The vector that the result will converge to is a scaled version of one of the eigenvectors of the matrix A.But which one ? The one with the largest eigenvalue among all eigenvectors not orthogonal to b.
https://en.wikipedia.org/wiki/Power_iteration