In mathematics, the Grassmannian G r k ( V ) {\displaystyle \mathbf {Gr} _{k}(V)} (named in honour of Hermann Grassmann) is a differentiable manifold that...

In mathematics, a Grassmannian may refer to: Affine Grassmannian Affine Grassmannian (manifold) Grassmannian, the classical parameter space for linear...

In mathematics, the Lagrangian Grassmannian is the smooth manifold of Lagrangian subspaces of a real symplectic vector space V. Its dimension is ⁠1/2⁠n(n...

In mathematics, the affine Grassmannian of an algebraic group G over a field k is an ind-scheme—a colimit of finite-dimensional schemes—which can be thought...

amplituhedron is defined as a mathematical space known as the positive Grassmannian. Amplituhedron theory challenges the notion that spacetime locality and...

space BU is the classifying space for stable complex vector bundles (a Grassmannian in infinite dimensions). One formulation of Bott periodicity describes...

point stabilizer general linear group): An = Aff(n, K) / GL(n, K). Grassmannian: Gr(r, n) = O(n) / (O(r) × O(n − r)) Topological vector spaces (in the...

bundle is a vector bundle occurring over a Grassmannian in a natural tautological way: for a Grassmannian of k {\displaystyle k} -dimensional subspaces...

In mathematics, there are two distinct meanings of the term affine Grassmannian. In one it is the manifold of all k-dimensional affine subspaces of Rn...

1 ( x ) = G d ( E x ) {\displaystyle p^{-1}(x)=G_{d}(E_{x})} is the Grassmannian of the d-dimensional vector subspaces of E x {\displaystyle E_{x}} ....

In mathematics, the Plücker map embeds the Grassmannian G r ( k , V ) {\displaystyle \mathbf {Gr} (k,V)} , whose elements are k-dimensional subspaces of...

space, which is roughly equivalent to describing the cohomology ring of Grassmannians. Sometimes it is used to mean the more general enumerative geometry...

the concept which is now known as a vector space. He introduced the Grassmannian, the space which parameterizes all k-dimensional linear subspaces of...

Institutions University of Manchester University of Cambridge Thesis Grassmannian Varieties / The Conic as a Space Element  (1932) Doctoral advisor H.F...

Gauss map can also be defined, and its target space is the oriented Grassmannian G ~ k , n {\displaystyle {\tilde {G}}_{k,n}} , i.e. the set of all oriented...

either a compact simple Lie group, a Grassmannian, a Lagrangian Grassmannian, or a double Lagrangian Grassmannian of subspaces of ( A ⊗ B ) n , {\displaystyle...

projective homogeneous variety, known as the isotropic Grassmannian or orthogonal Grassmannian OGr(r + 1, n + 2). (The numbering refers to the dimensions...

{\displaystyle Gr_{n}(V)} denote the Grassmannian, the space of n-dimensional linear subspaces of V, and denote the infinite Grassmannian G r n = G r n ( R ∞ ) {\displaystyle...

SU(p,q), A III 2pq Hermitian. Grassmannian of p subspaces of Cp+q. If p or q is 2; quaternion-Kähler Hermitian. Grassmannian of maximal positive definite...

the Grassmannian of n-planes in an infinite-dimensional complex Hilbert space; or, the direct limit, with the induced topology, of Grassmannians of n...

complex lines in Cn+1 passing through the origin. More generally, the Grassmannian G(k, V) of a vector space V over a field F is the moduli space of all...

of algebraic curves). Let V be a finite-dimensional vector space. The Grassmannian variety Gn(V) is the set of all n-dimensional subspaces of V. It is a...

reductive group G and certain equivariant perverse sheaves on the affine Grassmannian associated to G. This equivalence provides a non-combinatorial construction...

underlying vector space of dimension 4. It is now part of the theory of Grassmannians G r ( k , V ) {\displaystyle \mathbf {Gr} (k,V)} ( k {\displaystyle...

synthetic description as an incidence correspondence. Recall that the Grassmannian G r ( 1 , 2 ) {\displaystyle \mathbf {Gr} (1,2)} parametrizes the set...

algebraic geometry, a Schubert variety is a certain subvariety of a Grassmannian, G r k ( V ) {\displaystyle \mathbf {Gr} _{k}(V)} of k {\displaystyle...

R n + 1 ) {\displaystyle \mathbf {Gr} (1,\mathbb {R} ^{n+1})} ⁠ of a Grassmannian space. As with all projective spaces, ⁠ R P n {\displaystyle \mathbb...

Gradian, in geometry Gradshteyn and Ryzhik, a calculus reference work the Grassmannian, Gr k ⁡ ( V ) {\displaystyle \operatorname {Gr} _{k}(V)} General relativity...

give a concrete description of the Schubert cells associated with the Grassmannian of k {\displaystyle k} -dimensional subspaces of a vector space. If j...

Pracna, Petr (2015). "From Cayley-Dickson Algebras to Combinatorial Grassmannians". Mathematics. 3 (4). MDPI AG: 1192–1221. arXiv:1405.6888. doi:10.3390/math3041192...