Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I feel like this must have an obvious answer, but my knowledge of integer arithmetic is limited.

Given an (integer) matrix $A$ of dimension $m \times n$ and an unimodular matrix $U_l$ of dimension $m \times m$, does there always exist an unimodular matrix $U_r$ of dimension $n \times n$ such that $U_l \cdot A$ = $A \cdot U_r$ ?

If so, what is an efficient way to compute $U_r$ from $U_l$ (or the other way round) ?

share|cite|improve this question
up vote 2 down vote accepted

No. If $n=1$ and $m\ne1$, then $AU_r=\pm A$, whereas $U_lA$ isn't necessarily $\pm A$.

share|cite|improve this answer
Simple as that. Thanks. – Philippe Sep 26 '12 at 18:33

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.