/sci/ - Science & Math

I fucking love you. You have saved /sci/.

Thank you, EK. Really.

You are the best. There are no words to describe how amazing you are.

captcha: greatness herefsh

I am fucken happy right now!

Let <span class="math">A[/spoiler] and <span class="math">\mathbb{K}[/spoiler] be as above. The elementary divisors <span class="math">q_1,\dots,q_r \in\mathbb{K}[x][/spoiler] of <span class="math">A[/spoiler] are those normalized diagonal entries of the Smith normal form of the matrix <span class="math"> xI − A \in Mat(n,\mathbb{K})[/spoiler], which are not constant.

I can prove this, but the proof is rather involved, so I will just state the theorem here. :)