Given a square matrix $\mathbf{A}$, its eigenvalues $\lambda$ and eigenvectors $\vec{\mathbf{v}} $ are, by definition, the solutions to the following equation: $$ \mathbf{A} \cdot \vec{\mathbf{v}} = \lambda \cdot \vec{\mathbf{v}} $$
Say $\left\{\lambda_1, \lambda_2, \dots, \lambda_n\right\}$ is the set of eigenvalues and $\mathbf{\Lambda} $ is a diagonal matrix composed by these eigenvalues: $$ \mathbf{\Lambda} = \begin{bmatrix} \lambda_1 & 0 & \cdots & 0 \\ 0 & \lambda_2 & \cdots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \cdots & \lambda_n \\ \end{bmatrix} $$
Say $\left\{\vec{\mathbf{v}_1}, \vec{\mathbf{v}_2}, \dots, \vec{\mathbf{v}_n}\right\}$ is the set of eigenvectors and $\mathbf{V}$ is a square matrix composed by these eigenvectors: $$ \mathbf{V} = \begin{bmatrix} \vec{\mathbf{v}_1} & \vec{\mathbf{v}_2} & \cdots & \vec{\mathbf{v}_n} \end{bmatrix} $$
Then the eigenvalues-eigenvectores relation can be written in a matricial form: $$ \mathbf{A} \cdot \mathbf{V} = \mathbf{V} \cdot \mathbf{\Lambda} $$
However, I rarely see this format anywhere. Why? Is there something wrong with it?