Conditions 1 3 imply that the subgroup,, is basis of a vector space or a free abelian group.
2.
Moreover, if one uses several of them to form the basis of a vector space, the system can be n-dimensional.
3.
Since there is no preferred way to choose an ordered basis of a vector space, a frame bundle lacks a canonical choice of identity cross-section.
4.
In this setting, a "'frame "'carries the geometric idea of a basis of a vector space over to other sorts of geometrical spaces ( Klein geometries ).
5.
In linear algebra, a "'frame "'of an inner product space is a generalization of a basis of a vector space to sets that may be linearly dependent.
6.
Given a basis of a vector space " V ", every element of " V " can be expressed uniquely as a linear combination of basis vectors, whose coefficients are referred to as vector "'coordinates "'or "'components " '.
7.
A "'Schauder basis "'or "'countable basis "'is similar to the usual ( Hamel ) basis of a vector space; the difference is that for Hamel bases we use linear combinations that are " finite " sums, while for Schauder bases they may be " infinite " sums.
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