In mathematics, particularly in linear algebra, a flag is an increasing sequence of subspaces of a finite-dimensional vector space V. Here "increasing" means each is a proper subspace of the next (see filtration): The term flag is motivated by a particular example resembling a flag: the zero point, a line, and a plane correspond to a nail, a staff, and a sheet of fabric. If we write that dim Vi = di then we have where n is the dimension of V (assumed to be finite). Hence, we must have k ≤ n. A flag is called a complete flag if di = i for all i, otherwise it is called a partial flag.