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I tried with CPPLAPACK and dgeev routine:

http://cpplapack.sourceforge.net/

but only about 2/3 of eigen values and vectors are exact, for my project I need all vectory exactly calculated with the norm of unity, for the time expansion of my system in eigen space. I use MKL and ICC compiler, how can I calculate numerically all eigen vectors exactly in c++, which method would be exact.