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:
“There are two great rules in life, the one general and the other particular. The first is that every one can in the end get what he wants if he only tries. This is the general rule. The particular rule is that every individual is more or less of an exception to the general rule.”
—Samuel Butler (1835–1902)
“Men have an extraordinarily erroneous opinion of their position in nature; and the error is ineradicable.”
—W. Somerset Maugham (1874–1966)