A Few Matrix Applications
Example 2:
Let $A = \begin{bmatrix} 1 & 1 \\ 0 & 2 \end{bmatrix}$. Then:
$\det(A - \lambda I) = \det\begin{bmatrix} 1 - \lambda & 1 \\ 0 & 2 - \lambda \end{bmatrix} = (1 - \lambda)(2 - \lambda) - 1\cdot 0 = (1 - \lambda)(2 - \lambda)$
So the eigenvalues are $\lambda = 1, 2$.
Eigenvalues are widely used in computer science, including graph analysis, machine learning, and stability analysis of systems.
These notes by Miriam Briskman are licensed under CC BY-NC 4.0 and based on sources.