In geometry, Plücker coordinates, introduced by Julius Plücker in the 19th century, are a way to assign six homogeneous coordinates to each line in projective...

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

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

y_{2},y_{3},y_{4})} on the line. The Plücker embedding is the generalization of this to create homogeneous coordinates of elements of any dimension m {\displaystyle...

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...

Plücker matrix is a special skew-symmetric 4 × 4 matrix, which characterizes a straight line in projective space. The matrix is defined by 6 Plücker coordinates...

the origin. Plücker coordinates are a way of representing lines in 3D Euclidean space using a six-tuple of numbers as homogeneous coordinates. Generalized...

Julius Plücker introduced an alternative representation using two free vectors. This representation was finally named after Plücker. The Plücker representation...

system of homogeneous line coordinates in three-dimensional space called Plücker coordinates. Six numbers in a set of coordinates only represent a line when...

the lines of action of forces. The pair of vectors that form the Plücker coordinates of a line define a unit screw, and general screws are obtained by...

polyhedron with a line. Plücker coordinates#Plane-line meet calculating the intersection when the line is expressed by Plücker coordinates. Plane–plane intersection...

of the Grassmannian G(2, 4) (embedded in projective space P5 by Plücker coordinates) with a hypersurface. It is called a line complex because points...

geometry in space over a field of characteristic 0, Conwell used Plücker coordinates in PG(5,2) and identified the points representing lines in PG(3,2)...

use of quasi-Plücker coordinates, which parametrize noncommutative Grassmannians and flags in much the same way as Plücker coordinates do Grassmannians...

decomposed into a rotation about and a slide along this screw axis. Plücker coordinates are used to locate a screw axis in space, and consist of a pair of...

exterior square Λ2V of V. The line coordinates obtained this way are known as Plücker coordinates. These Plücker coordinates satisfy the quadratic relation...

\end{aligned}}} These are known as the Plücker coordinates of the line, though they are also an example of Grassmann coordinates. A line as the intersection of...

latter space has a distinguished system of homogeneous coordinates, given by the Plücker coordinates. An effective algebraic cycle in P n − 1 {\displaystyle...

the algebras of homogeneous functions on the Grassmannians. The Plücker coordinates provide some of the distinguished elements. For the Grassmannian...

^{2}\mathbb {R} ^{3,1}} for the set of bivectors in spacetime. The Plücker coordinates are bivectors in R 4 {\displaystyle \mathbb {R} ^{4}} while the electromagnetic...

can be naturally assigned Plücker coordinates (p12, p13, p14, p23, p24, p34) where pij = aibj − ajbi, and the line coordinates satisfy p12 p34 + p13 p24...

of the displacement of this body transforms Plücker coordinates in the moving frame to Plücker coordinates in the fixed frame by the formula[clarification...

{\displaystyle {\boldsymbol {e}}_{30}} gives the necessary elements for (Plücker) coordinates of lines. With the geometric product having been defined a transform...

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

are 35 lines in all. The lines of PG(3,2) are identified by their Plücker coordinates in PG(5,2) with 63 points, 35 of which represent lines of PG(3,2)...

position and orientation. It also plots coordinate frames, supports Plücker coordinates to represent lines, and provides support for Lie group operations...

In geometry, Plücker's conoid is a ruled surface named after the German mathematician Julius Plücker. It is also called a conical wedge or cylindroid;...

4-Dimensional problem. To tackle this, solutions are often performed using Plücker coordinates, which effectively linearize the problem in a 5D projective space...

their coordinates and therefore belong to the Euclidean plane. An explicit quartic with twenty-eight real bitangents was first given by Plücker (1839)...

noncommutative symmetric functions The introduction of noncommutative Plücker coordinates Noncommutative integrable systems He was included in the 2019 class...