Prove that matrix $A = \sum_k^{n}x_k\lambda_ky_k^T$

Question

Prove that matrix $\ A = \sum_{k=1}^n {\bf x}_k \lambda_k {\bf y}_k^T.\ $ If $\ {\bf x}_k\ $ and $\ {\bf y}_k\ $ are the corresponding eigenvector from the left and from the right of $\lambda_k$. Any idea how to start on this proof? Also $A\in\mathbb{R}^{n\times n}$.