What is the dimension and the number of basis vectors for a subspace of 3×3 symmetric matrices?
Earlier my professor told us that the dimension and the number of basis vectors for a subspace are the same. And I did get that as they are the vectors that can span the whole subspace.But when describing the subspace of symmetric matrices he says when counting the basis vectors we only consider the diagonal elements and the entries either above or below. I get that if you specify the entries above the diagonal the entries below it will be the same and so if you take a 3×3 matrix, you only need to specify 6 entries.But aren't the matrices still containing all nine entries then how is it that the subspace is 6D and not 9D?
