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:
“The bond between a man and his profession is similar to that which ties him to his country; it is just as complex, often ambivalent, and in general it is understood completely only when it is broken: by exile or emigration in the case of one’s country, by retirement in the case of a trade or profession.”
—Primo Levi (1919–1987)
“It is in vain that we would circumscribe the power of one half of our race, and that half by far the most important and influential. If they exert it not for good, they will for evil; if they advance not knowledge, they will perpetuate ignorance. Let women stand where they may in the scale of improvement, their position decides that of the race.”
—Frances Wright (1795–1852)