I've been reading this proof of Jordan's theorem:
<http://www.cs.uleth.ca/~holzmann/notes/jordan.pdf>

and there are a few questions I hope you could answer for me.

Firstly, why $(A\_{\lambda})\_{\mu \_i} = A \_{\lambda + \mu \_{i}} =: A \_{\lambda\_{ \ i}}$

and secondly, how do we know that $\dim (W \cap Ker A\_{\lambda}) \ge 1$?

The problem in the first question is that I'm not sure what $(A\_{\lambda})\_{\mu \_i}$ means.

Thank you.

I understand that we pick a vector $v\neq 0$ with an eigenvalue $\lambda$. $A$ is $n \times n$

$A\_{\lambda} = A - \lambda I \ \ \ \ \ \ \ \ \ A\_{\lambda}v=0,$ so we have $r = \dim \ker A\_{\lambda}>0$ 

$\dim \ range A\_{\lambda} = n-r<n $ , $W := range \ A\_{\lambda} $

I undestand that because $W := range \ A\_{\lambda} $, then $ A\_{\lambda} (W) \subset W$, so 
$A\_{\lambda} $ induces $T: W \rightarrow W$ and we can apply inductive hipothesis to its matrix. What I don't understand is why all of a sudden there are $\lambda\_i$ over the arrows and it is probably because I don't know what $(A\_{\lambda})\_{\mu \_i}$ means