My aim is to proceed with a Heuristic calculation of the Tangent space to Aut(V) at the identity. However, I will have to prove the problem statement before I can proceed with that.
My problem, Understanding the polynomial structure on the group Aut(V). The proper way of doing that would have to do with the symmetric algebra on the dual space, I don't wish to proceed this way.
And I have been told to visualize the "coordinates" of the matrices as polynomials and work with that. If that is so, what would it mean for the "coordinate" to be "zero". Once this is certified I can proceed. This is what I have thought.
Any other procedure, please, please let me know.