I know that $A\textbf{x}=\lambda \textbf{x}$, where $\textbf{x}$ is right eigenvector, while in $\textbf{y}A =\lambda \textbf{y}$, $\textbf{y}$ is left eigenvector.
But What is significance of left and right eigenvectors ? How do they differ from each other geometrically?