Matlab exists for Linux and is the same as on Windows. LibreOffice is a fully functioning office suit for Linux.
I can't speak to SOLIDWORKS, their website only lists a windows version. There is however some community work being done here https://github.com/cryinkfly/SOLIDWORKS-for-Linux And it looks like they have it running.
Given that Fedora and Ubuntu are listed on that github, you should probably start with either one of those.
For a complete beginner I'd recommend Ubuntu, since it's a solid distro with huge wealth on online support available.