Eigenvectors and eigenvalues
Linear algebra talks about functions, which are often called transformations. In that context, an eigenvector is a vector, different from the null vector which does not change direction in the transformation (except if it turns the vector exactly around). The vector may change its length, or become null. The value of the change in length of the vector is known as eigenvalue.
In other words, if matrix A times the vector v is equal to the scalar λ times the vector v, than λ is the eigenvalue of v, where v is the eigenvector.