Flags in A Vector Space
A flag in a finite dimensional vector space V over a field F is an increasing sequence of subspaces, where "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. Hence, we must have k ≤ n. A flag is called a complete flag if di = i, otherwise it is called a partial flag. The signature of the flag is the sequence (d1, … dk).
A partial flag can be obtained from a complete flag by deleting some of the subspaces. Conversely, any partial flag can be completed (in many different ways) by inserting suitable subspaces.
Read more about this topic: Generalized Flag Variety
Famous quotes containing the words flags in, flags and/or space:
“No doubt I shall go on writing, stumbling across tundras of unmeaning, planting words like bloody flags in my wake. Loose ends, things unrelated, shifts, nightmare journeys, cities arrived at and left, meetings, desertions, betrayals, all manner of unions, adulteries, triumphs, defeats ... these are the facts.”
—Alexander Trocchi (1925–1983)
“No doubt I shall go on writing, stumbling across tundras of unmeaning, planting words like bloody flags in my wake. Loose ends, things unrelated, shifts, nightmare journeys, cities arrived at and left, meetings, desertions, betrayals, all manner of unions, adulteries, triumphs, defeats ... these are the facts.”
—Alexander Trocchi (1925–1983)
“The woman’s world ... is shown as a series of limited spaces, with the woman struggling to get free of them. The struggle is what the film is about; what is struggled against is the limited space itself. Consequently, to make its point, the film has to deny itself and suggest it was the struggle that was wrong, not the space.”
—Jeanine Basinger (b. 1936)