Eigen is primarily MPL2 licensed. See COPYING.MPL2 and these links:
Some files contain third-party code under BSD or LGPL licenses, whence the other COPYING.* files here.
All the LGPL code is either LGPL 2.1-only, or LGPL 2.1-or-later. For this reason, the COPYING.LGPL file contains the LGPL 2.1 text.
If you want to guarantee that the Eigen code that you are #including is licensed under the MPL2 and possibly more permissive licenses (like BSD), #define this preprocessor symbol:
EIGEN_MPL2_ONLY
For example, with most compilers, you could add this to your project CXXFLAGS:
-DEIGEN_MPL2_ONLY
This will cause a compilation error to be generated if you #include any code that is LGPL licensed.