A set of at least points in -dimensional Euclidean space is said to be in general linear position (or just general position) if no hyperplane contains more than points — i.e. the points do not satisfy any more linear relations than they must. A set containing points for is in general linear position if and only if no -dimensional flat contains all points.
A set of points in general linear position is also said to be affinely independent (this is the affine analog of linear independence of vectors, or more precisely of maximal rank), and points in general linear position in affine d-space are an affine basis. See affine transformation for more.
Similarly, n vectors in an n-dimensional vector space are linearly independent if and only if the points they define in projective space (of dimension ) are in general linear position.
If a set of points is not in general linear position, it is called a degenerate case or degenerate configuration — they satisfy a linear relation that need not always hold.
A fundamental application is that, in the plane, five points determine a conic, as long as the points are in general linear position (no three are collinear).
Read more about this topic: General Position
Famous quotes containing the words general and/or position:
“At Hayes’ General Store, west of the cemetery, hangs an old army rifle, used by a discouraged Civil War veteran to end his earthly troubles. The grocer took the rifle as payment ‘on account.’”
—Administration for the State of Con, U.S. public relief program (1935-1943)
“I think the most important education that we have is the education which now I am glad to say is being accepted as the proper one, and one which ought to be widely diffused, that industrial, vocational education which puts young men and women in a position from which they can by their own efforts work themselves to independence.”
—William Howard Taft (1857–1930)