Eigen - versatile, fast, reliable linear algebra library for C++

After years of trudging along with all manners of legacy libraries for vector math, both homegrown and 3rd party, I finally got turned on to Eigen by a coworker. Unfortunately I can't provide any first impressions of it yet - I've been too giddy over all the cool features (vectorization! loop unrolling! lazy evaluation! elegance! it's free!) to actually be able to sit down and try it out. Instead, I present you with the product overview verbatim from their website:

• Eigen is versatile.
  • It supports all matrix sizes, from small fixed-size matrices to arbitrarily large dense matrices, and even sparse matrices.
  • It supports all standard numeric types, including std::complex, integers, and is easily extensible to custom numeric types.
  • It supports various matrix decompositions and geometry features.
  • Its ecosystem of unsupported modules provides many specialized features such as non-linear optimization, matrix functions, a polynomial solver, FFT, and much more.
• Eigen is fast.
  • Expression templates allow to intelligently remove temporaries and enable lazy evaluation, when that is appropriate.
  • Explicit vectorization is performed for SSE 2/3/4, ARM NEON, and AltiVec instruction sets, with graceful fallback to non-vectorized code.
  • Fixed-size matrices are fully optimized: dynamic memory allocation is avoided, and the loops are unrolled when that makes sense.
  • For large matrices, special attention is paid to cache-friendliness.
• Eigen is reliable.
  • Algorithms are carefully selected for reliability. Reliability trade-offs are clearly documented and extremely safe decompositions are available.
  • Eigen is thoroughly tested through its own test suite (over 500 executables), the standard BLAS test suite, and parts of the LAPACK test suite.
• Eigen is elegant.
  • The API is extremely clean and expressive while feeling natural to C++ programmers, thanks to expression templates.
  • Implementing an algorithm on top of Eigen feels like just copying pseudocode.
• Eigen has good compiler support as we run our test suite against many compilers to guarantee reliability and work around any compiler bugs. Eigen also is standard C++98 and maintains very reasonable compilation times.