There are many libraries for C++ that can be used to compute Eigenvectors and Eigenvalues. However, if you are already using OpenCV in your project, then it can be used to get these values easily by using the PCA class. This class is declared in
opencv2/core/core.hpp header file and defined in the
modules/core/src/matmul.cpp source file.
Here is an example:
Tried with: OpenCV 2.4.9 and Ubuntu 14.04