Why is this expression: $\begin{pmatrix} \frac{k+mg}{l} & -k\\ -k & \frac{k+mg}{l} \end{pmatrix} \begin{pmatrix} \rho_1\\\rho_2 \end{pmatrix}=\omega^2\begin{pmatrix} m & 0\\ 0 & m \end{pmatrix} \begin{pmatrix} \rho_1\\\rho_2 \end{pmatrix}$
a matricial form for equation for eigenvalues and eigenvectors? I was told that the generical expression of the equation for eigenvalues and eigenvectors is $A\bf{x}=\lambda \bf{x}$... How can I obtain eigenvalues and eigenvectors from the first expression that I have written? Thank you!