Is there someplace in the documentation that explains when Eigen uses row major or column major formats? Is there a way to tell at runtime where a matrix is in one format or the other? Thanks!

The default is column major and you cannot select one storage format at runtime. This must be specified at compile time via the 4th template argument of Matrix, eg:

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Matrix

Note that if you write a template function taking an Eigen matrix or expression, then you can query the storage format like this:

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template void foo(const MatrixBase& m)
{
  const bool isRowMajor = inf(Derived::Flags)&RowMajorBit;
  ...
}