What would be the best way to describe/explain to someone that knows nothing about math what eigenvalue and eigenvector are?
If you have an equation $\displaystyle \displaystyle \mathbf{A}\mathbf{x} = \lambda \mathbf{x}$, where A is a matrix, x is a column vector and lambda is a constant, the eigenvalues are the lambda values which make this equation true, and the eigenvectors are the particular vectors x which make the equation true. Obviously each eigenvector is associated with a particular eigenvalue.