Eigen

Eigen is a template library focused on covering dense and sparse linear algebra, including numerical solvers, matrices and other related algorithms. Since this is a pure template library defined in the headers, it does not need anything else than the C++ standard library, so you can start using it right away. 

According to the developer, there are several features that make the template stand out, one of the most noteworthy being its versatility. To put it simply, the library comes with wide support and is compatible with all standard numeric types and matrices along with other related operations. The tool is thoroughly and frequently tested via a dedicated suite featuring over 500 executables, so it should be reliable in most situations. The results of the tests are available on the home page, so feel free to check them out anytime. 

Take note that the tool is a standard C++98 so it should also be compatible with most compilers. In fact, the developer claims they are running regular tests against many compilers out there, including the new ones. It is designed with C++ in mind, so if you are a developer using this language, working with it should flow naturally. As the developer puts it, implementing an algorithm feels like pseudocoding.