Hyperplane Section
Versandkostenfrei!
Versandfertig in 6-10 Tagen
22,99 €
inkl. MwSt.
PAYBACK Punkte
11 °P sammeln!
High Quality Content by WIKIPEDIA articles!In mathematics, a hyperplane section of a subset X of projective space Pn is the intersection of X with some hyperplane H in other words we look at the subset XH of those elements x of X that satisfy the single linear condition L = 0 defining H as a linear subspace. Here L or H can range over the dual projective space of non-zero linear forms in the homogeneous coordinates, up to scalar multiplication. From a geometrical point of view, the most interesting case is when X is an algebraic subvariety for more general cases, in mathematical analysis, some...
High Quality Content by WIKIPEDIA articles!In mathematics, a hyperplane section of a subset X of projective space Pn is the intersection of X with some hyperplane H in other words we look at the subset XH of those elements x of X that satisfy the single linear condition L = 0 defining H as a linear subspace. Here L or H can range over the dual projective space of non-zero linear forms in the homogeneous coordinates, up to scalar multiplication. From a geometrical point of view, the most interesting case is when X is an algebraic subvariety for more general cases, in mathematical analysis, some analogue of the Radon transform applies. In algebraic geometry, assuming therefore that X is V, a subvariety not lying completely in any H, the hyperplane sections are algebraic sets with irreducible components all of dimension n 1. What more can be said is addressed by a collection of results known collectively as Bertini's theorem.
