Fix an ordered basis for "V", identifying it with F"n", whose general linear group is the group GL("n",F) of "n" × "n" invertible matrices. The standard flag associated with this basis is the one where the "i" th subspace is spanned by the first "i" vectors of the basis. Relative to this basis, the stabilizer of the standard flag is the group of nonsingular lower triangular matrices, which we denote by "B""n". The complete flag variety can therefore be written as a homogeneous space GL("n",F) / "B""n", which shows in particular that it has dimension "n"("n"−1)/2 over F.