This is a frequently asked feature. Thanks to IndexedView, we can easily implement it as:

template<typename XprType, typename RowFactorType, typename ColFactorType>
auto repelem(const XprType &xpr, RowFactorType row_factor, ColFactorType col_factor) {
    using namespace Eigen;

    const int RowFactor = internal::get_fixed_value<RowFactorType>::value;
    const int ColFactor = internal::get_fixed_value<ColFactorType>::value;
    const int NRows = XprType::RowsAtCompileTime == Dynamic || RowFactor == Dynamic ? Dynamic : XprType::RowsAtCompileTime*RowFactor;
    const int NCols = XprType::ColsAtCompileTime == Dynamic || ColFactor == Dynamic ? Dynamic : XprType::ColsAtCompileTime*ColFactor;
    const int nrows = internal::get_runtime_value(row_factor) * xpr.rows();
    const int ncols = internal::get_runtime_value(col_factor) * xpr.cols();

    return xpr(
        Array<int,NRows,1>::LinSpaced(nrows,0,xpr.rows()-1),
        Array<int,NCols,1>::LinSpaced(ncols,0,xpr.cols()-1)
    );
}

Full demo: https://godbolt.org/z/rYgDxF

This can easily be turned as a member function and specialized for Horizontal or Vertical replication only.

What would be a good name given that we already have "replicate" as an equivalent to "repmat" ?

Can we do better than the above implementation if using a dedicated expression (as for replicate)?