When I define the following function:
template <typename Derived>

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void DoMany( std::vector< Eigen::MatrixBase<Derived> > & destVec )
{}


I can't get this calling code to compile:
std::vector< Eigen::MatrixXf > xx;
DoMany( xx);

Shouldn't I be able to do something like that?

This does not make sense because Eigen::MatrixBase<Derived> is an abstract base class. You cannot construct object of type Eigen::MatrixBase<Derived>. Simply make "DoMany" more generic:

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template<typename MatType>
vod DoMany(std::vector<MatType>&);