Every intersection of projective subspaces is a projective subspace. Consequently, sets of parallel affine subspaces remain parallel after an affine transformation. Intuitively, we glob together the Jordan block invariant subspaces corresponding to the same eigenvalue. They are called affine properties and include the concepts of lines, subspaces, and parallelism. Rado theorem and its analogue for intersecting families of subspaces over finite fields. States associated with these other irreducible subspaces are called parastatistic states. There are however more types of irreducible subspaces. Young tableaux provide a way to classify all of these irreducible subspaces. All sequence spaces are linear subspaces of this space. This is equivalent to and being orthogonal as subspaces of . The simplest instance is PG(3,2) which has Fano planes as its 2-dimensional subspaces. The concept of line generalizes to planes and higher-dimensional subspaces. Some vector spaces can be decomposed into direct sums of subspaces. Geometrically, the degrees of freedom can be interpreted as the dimension of certain vector subspaces. The counterpart to subspaces are "quotient vector spaces".