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> ...makes a lot of the abstractions basically "free"

Maybe it is just me, but I do not really see the need for "abstractions" in a linear algebra library. Numbers are already an abstraction, you do not want to hide them! Ok, maybe you want to choose between "float" and "double", but this does not merit all that overcomplication.

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The abstractions inside Eigen are there to enable powerful compile time optimisations, such as compiling the addition of three vectors `Eigen::VectorXf x = a + b + c;` in a single loop instead of naively allocating a temporary to evaluate `Eigen::VectorXf tmp = b + c;` then evaluating `Eigen::VectorXf x = a + tmp;`.

This logic is omnipresent in Eigen and is crucial to its performance. It is also used to have specialized versions of some decompositions when the matrix's size is known at compile time.

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