Eigenvalues and eigenvectors

orochimaru
hi,
i have trouble understanding these two terms.
can anyone explain to me eigenvalues and eigenvectors in laymen terms?

Galileo
Generally this vector Ax will be some different vector, one that is linearly independent from v (it points in another direction). However if it is some scalar multiple of v (so $Av=\lambda v$ for some scalar $\lambda$ then v is called an eigenvector (the nullvector is ruled out as an eigenvector by definition) and $\lambda$ is its corresponding eigenvalue.