This is a very incomplete list of libraries that you have to know about. Most of these have been discovered and used during my M.Sc or private projects. I have contributed and written some of them and the others are just libraries that I like.
Maths and Optimisation:
- Eigen – This is by far the best Matrix and Vector toolkit on the face of the planet. It is entirely implemented in C++ templates which means there are zero issues compiling on any platform. It also has SIMD optimisations for both X86 and ARM NEON platforms. Eigen is used in some big projects and has all the main factorisation algorithms built in.