Jordan Block

When we have to use Jordan Form, we need to use a Jordan block Where we have repeated eigenvalues, $\lambda$.

This is from setting up an equation like this

$$\boxed{\begin{array}{rl}A{v}_1& =v_1{\lambda }_1\\ A{v}_2& =v_1\cdot 1+v_2{\lambda }_1\end{array}}$$