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 has always been the same amount of light in the world. The new and missing stars, the comets and eclipses, do not affect the general illumination, for only our glasses appreciate them.”
—Henry David Thoreau (1817–1862)
“The Americans are violently oral.... That’s why in America the mother is all-important and the father has no position at all—isn’t respected in the least. Even the American passion for laxatives can be explained as an oral manifestation. They want to get rid of any unpleasantness taken in through the mouth.”
—W.H. (Wystan Hugh)