is called a flag in . We speak of a complete flag when
for each .
we say that a list of vectors is an adapted basis relative to the flag, if the first vectors give a basis of , the first vectors give a basis of , etc. Thus, an alternate characterization of a complete flag, is that the first elements of an adapted basis are a basis of .
Let us consider . For each let be the span of , where denotes the basic vector, i.e. the column vector with in the position and zeros everywhere else. The give a complete flag in . The list is an adapted basis relative to this flag, but the list is not.
More generally, a flag can be defined as a maximal chain in a partially ordered set. If one considers the poset consisting of subspaces of a (finite dimensional) vector space, one recovers the definition given above.
|Date of creation||2013-03-22 12:42:35|
|Last modified on||2013-03-22 12:42:35|
|Last modified by||rmilson (146)|