Eigenvectors and eigenvalues are concepts in linear algebra. An eigenvector of a linear transformation is a vector that only changes by a scale factor under that transformation, not changing direction. This scale factor is the corresponding eigenvalue. For example, in the matrix equation AX = λX, if X is an eigenvector and λ is the eigenvalue, then applying the linear transformation A scales X by λ but does not change its direction. Examples are given of linear transformations that shift points along an axis by distances proportional to their original distances from the axis, with eigenvectors being vectors that do not change direction under this transformation.
