number of quadrics defined by the § Plücker relations (see below). The Plücker embedding was first defined by Julius Plücker in the case k = 2 , n = 4 {\displaystyle...

parameterizing them by what are now called Plücker coordinates. (See § Plücker coordinates and Plücker relations below.) Hermann Grassmann later introduced...

to Julius Plücker. Julius Plücker at the Mathematics Genealogy Project The Cathode Ray Tube site Weisstein, Eric Wolfgang (ed.). "Plücker, Julius (1801–1868)"...

embedding into a sufficiently large projective space. This is a direct generalization of the construction of a Grassmannian variety via the Plücker embedding...

y 4 ) {\displaystyle (y_{1},y_{2},y_{3},y_{4})} on the line. The Plücker embedding is the generalization of this to create homogeneous coordinates of...

{M} } is embedded in P 5 ≅ P ( ∧ 2 T ) {\displaystyle \mathbf {P} _{5}\cong \mathbf {P} (\wedge ^{2}\mathbb {T} )} by the Plücker embedding; the image...

k}(V){\bigr )}} . This is called the Plücker embedding, and the image of the embedding can be characterized by the Plücker relations. The exterior algebra...

text and embedded images, for offline mobile reading. Free and open-source software portal Wikipedia:Snapshots – 2000 Wikipedia articles in Plucker format...

the multiplication being the tensor product. Plücker embedding The Plücker embedding is the closed embedding of the Grassmannian variety into a projective...

\wedge w_{k}\in \textstyle \bigwedge ^{\!k}V} corresponds by the Plücker embedding to the subspace W {\displaystyle W} with oriented basis w 1 , … ,...

subspaces of V. It is a projective variety: it is embedded into a projective space via the Plücker embedding: { G n ( V ) ↪ P ( ∧ n V ) ⟨ b 1 , … , b n ⟩ ↦...

the product of projective varieties over k is again projective. The Plücker embedding exhibits a Grassmannian as a projective variety. Flag varieties such...

Grassmannian, and the Hirota equations as expressing the Plücker relations, characterizing the Plücker embedding of the Grassmannian in the projectivization of...

choose an orthonormal basis for ⁠ W {\displaystyle W} ⁠, then the Plücker embedding gives a vector in the exterior algebra but only up to scaling. Using...

and 682-684). Grassmann manifold Hardy space Homogeneous polynomial Plücker embedding Beauzamy, Bernard; Bombieri, Enrico; Enflo, Per; Montgomery, Hugh...

{F}}} . The Plücker coordinates { π λ ( w ) } {\displaystyle \{\pi _{\lambda }(w)\}} satisfy an infinite set of bilinear relations, the Plücker relations...

\Omega } the space of ω A {\displaystyle \omega ^{A}} . Under the Plücker embedding, the tractor bundle in four dimensions is isomorphic to the exterior...

clasts embedded in glacial ice passing over bedrock and grinding down the top of the rock into a smoother surface. The small rocks entrained by plucking act...

equilateral-triangle version of the Möbius strip. This flat triangular embedding can lift to a smooth embedding in three dimensions, in which the strip lies flat in three...

Hilbert scheme can be embedded into projective space as a subscheme of a Grassmannian (which is projective via the Plücker embedding). The general linear...

algebra Niels Henrik Abel Carl Gustav Jacob Jacobi Jakob Steiner Julius Plücker Arthur Cayley Bernhard Riemann Max Noether William Kingdon Clifford David...

G_{d}(E)\to \mathbb {P} (\wedge ^{r}E)} , which is nothing but a family of Plücker embeddings. The relative tangent bundle TGd(E)/X of Gd(E) is given by T G d (...

the ring of polynomials on the image of a Grassmannian under the Plücker embedding. For given d ≤ n we define as formal variables the brackets [λ1 λ2...

in 1990, "As I write a song, I write some of the instrumental piano and pluck some of the different notes for the arrangement. It's impossible to lay...

pyramid spikes embedded in his chest, The Chosen One makes wooden dummies, embeds similar spikes onto their chests and attempts to pluck them out with...

Tetrahedroids, special Kummer surfaces Wave surface, a special tetrahedroid Plücker surfaces, birational to Kummer surfaces Weddle surfaces, birational to...

geometry. Klein received his doctorate, supervised by Plücker, from the University of Bonn in 1868. Plücker died in 1868, leaving his book concerning the basis...

extensively in West Africa. A kora typically has 21 strings, which are played by plucking with the fingers. It has features of the lute and harp. The kora is built...

singular point on a curve is one where the curve is not given by a smooth embedding of a parameter. The precise definition of a singular point depends on...

usually held flat against the player's body and played by strumming or plucking the strings with the dominant hand, while simultaneously pressing selected...