A contest paper cites the following theorem as a theorem of Frobenius:
Let $A$ be a $m \times n$ integer-valued matrix. There exists a positive integer $r \leq \min(m,n)$ and two unimodular matrices $P,Q$ such that $$PAQ = \text{diag}(d_1,d_2,...,d_r,0,0,...,0),$$ where each $d_i$ divides $d_{i+1}.$
Where can I read more about this result? I'm looking for a proof, and eventually some context.
I have not encountered this theorem before, but with some searching I found these links:
First this, which explains the history of the theorem
and then this which gives information about the theorem (such matrices are in Smith Normal Form):
and here are some proofs of it:
Here is a paper with a bunch of theoerms leading up to the construction of Smith normal form:
http://www.numbertheory.org/courses/MP274/smith.pdf
and here is Smith's actual paper presenting his ideas (quite complex and hard to read) regarding this normal form:
https://www.jstor.org/stable/108738