Prove that if y is a linear functional on an n-dimensional vector space V, then the set of all those vectors x for which [x,y]=0 is a subspace of V; what is the dimension of that subspace?
Let X be the set of vectors x in V for which [x,y]=0 where y is a linear functional. Let be any two vectors in X and let be arbitrary scalars. Then,
and so X is a subspace of V.
Don't know the dimension, maybe n-1