1. The problem statement, all variables and given/known data Hello guys; I am currently dealing with a problem that I have faced before several times and I would like to know a consistent way on how to solve it. I think what I want to do is diagonalize a matrix but I'm not sure if that's exactly it. Basically I have two or three equations of motion and I want to put them in a good matrix form in order to begin finding solutions. In this particular problem I have three equations of motion and the book I'm using puts them in to a nice matrix form right away and I'm not sure how to get there. Here is a picture of what they've done: I know how to create these matrices for 'm' and 'k' when they are more symmetric if you will but I don't know how to make it nice like this. This will help me so much on other problems I also have to deal with. For some stupid reason I've ran in to this wall multiple times. Thanks in advance. 2. Relevant equations 3 equations of motion put in to a nice diagonalized matrix 3. The attempt at a solution I just don't understand how to get it into this nice 'diagonalized(?)' matrix form. If anyone can help out, this will greatly help me in the future.