Just a heads up, if you're looking for an open source routing software, gEDA and Oregano are good options. The UI is no where near as nice as eagle's. I kind of enjoyed gEDA though. They also has rather anemic libraries if you deviate from standard issue parts, just like eagle. I think these should be a good start on that front.
On to matlab, have you tried scilab? Once again, not quite what you're asking for but it is open-source and can calculate matrices.
In general, I cannot recommend open-source physics stuff to people due to UI issues. Physics students want results and many are not all that comfortable with a computer. I am not trying to flamebait, I actually applaud you in your interest in these products. I feel that need a bit more polish before being able to seriously threaten the big boys.
A simple suggestion or two: if you're using ubuntu/debian, apt-get the packages, they are friendly and install nicely. Also, www.osalt.com is an interesting site to see if there are good open-source projects out there.