Eigenvalues and eigenvectors arise when we study how linear transformations act on space. In simple terms, an eigenvector is a special direction that does not change direction under a transformation, although it may stretch, shrink, or flip. The amount by which it is scaled is called the eigenvalue. This idea is powerful because most transformations distort space in complicated ways, but eigenvectors reveal the hidden structure within that distortion. Instead of tracking how every point moves, w