Definition In mathematics, particularly in linear algebra, a flag is an increasing sequence of subspaces of a vector space V. Here "increasing" means each is a proper subspace of the next (see filtration): If we write the dim Vi = di then we have where n is the dimension of V (assumed to be finite-dimensional). Hence, we must have k ≤ n. A flag is called a complete flag if di = i, otherwise it is called a partial flag.
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