Hey, quick question... if I am considering the set of nxn matrices of determinant 1 (the special linear group), is it correct if I say that the set is a submanifold in the (n^2)-dimensional space of matrices because the determinant function is a constant function, so its derivative is zero everywhere? Also, I've been told that the tangent space to this set at the identity is just the space of trace 0 matrices, but I'm not seeing where this relationship comes from. Any help?(adsbygoogle = window.adsbygoogle || []).push({});

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# The Special Linear Group

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