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Questions about the properties of vector spaces and linear transformations, including linear systems in general.
1
vote
"A gentleman never chooses a basis."
there is a canonical map $ev:V \to V^{**}$ defined by $ev(v)(\phi) = \phi(v)$. to check that it is an isomorphism in the finite dimensional setting you can just check that it is injective and this is …
1
vote
Request for info on the space of commuting matrices preserving a flag.
for the case where n = 2 and the complete flag the variety in question is isomorphic to A^2 x Spec C[x,y]/(xy). so the space is not nec. smooth.