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 have a problem with a matrix equation/transformation problem which I need solving.

I have two transformations $A_1$ and $A_2$, both of which can be expressed as $A_i = R_i \times B_i$, $R_i$ denoting rotation. I want to solve the equation $$ R_{12}\times B_{12} = A_1 \times A_2^{-1} $$ for $R_{12}$ when $B_{12} = B_1 \times B_2^{-1} = R_1^{-1} \times A_1 \times A_2^{-1} \times R_2$.

The original transformations $A_1$ and $A_2$ are limited to rotation/scaling/translation. I could decompose the resulting transformation, but I'd prefer to avoid that since the solution isn't unique.

Is there a nice solution to this? It's been years and years since I last touched matrix algebra, so I don't remember all the nifty rules I was taught as an undergrad.

A numerical solution would be fine, but I'd prefer a analytical solution.

share|cite|improve this question
up vote 1 down vote accepted

It sounds like you know $B_{12}$. Therefore, you should be able to invert it and multiply both sides on the right by its inverse.

share|cite|improve this answer
Direct solution requires at least two of the three know for each $i$: $A_i$, $B_i$, $R_i$. – Emily Oct 19 '12 at 17:03
Muphrid's answer is absolutely correct. Now I feel stupid... – endolphins Oct 19 '12 at 17:08

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.