A Few Matrix Applications
Example 1:
Let $A = \begin{bmatrix} 2 & 0 \\ 0 & 3 \end{bmatrix}$. Then:
$\det(A - \lambda I) = \det\begin{bmatrix} 2 - \lambda & 0 \\ 0 & 3 - \lambda \end{bmatrix} = (2 - \lambda)(3 - \lambda)$
Setting this equal to $0$, we get $\lambda = 2, 3$.
These notes by Miriam Briskman are licensed under CC BY-NC 4.0 and based on sources.