11. A projective linear subspace of this projective space is called a linear system of divisors. 12. Because the eigenspace " E " is a linear subspace , it is commutative. 13. Flats are similar to linear subspaces , except that they need not pass through the origin. 14. Choose rational normal curves in these two linear subspaces , and choose an isomorphism ? between them. 15. Menger and Birkhoff gave axioms for projective geometry in terms of the lattice of linear subspaces of projective space. 16. If is a-linear functional on a-linear subspace of which is dominated by on in absolute value, 17. If is a closed linear subspace in, one can associate the " orthogonal of " in the dual, 18. A " homogeneous subspace " of a super vector space is a linear subspace that is spanned by homogeneous elements. 19. One can find linear subspaces or discrete groups that are lattices in a subspace, depending on how one takes a limit. 20. Adding a fixed vector to the elements of a linear subspace of a vector space produces an " affine subspace ".
