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:
“You don’t want a general houseworker, do you? Or a traveling companion, quiet, refined, speaks fluent French entirely in the present tense? Or an assistant billiard-maker? Or a private librarian? Or a lady car-washer? Because if you do, I should appreciate your giving me a trial at the job. Any minute now, I am going to become one of the Great Unemployed. I am about to leave literature flat on its face. I don’t want to review books any more. It cuts in too much on my reading.”
—Dorothy Parker (1893–1967)
“The essence of spirit, he thought to himself, was to choose the thing which did not better one’s position but made it more perilous. That was why the world he knew was poor, for it insisted morality and caution were identical.”
—Norman Mailer (b. 1923)