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Grassmannian

In mathematics, a Grassmannian G r k ( V ) {\displaystyle \mathbf {Gr} _{k}(V)} , also known as a Grassmann manifold, is a differentiable manifold that parameterizes the set of all k {\displaystyle k} -dimensional linear subspaces of an n {\displaystyle n} -dimensional vector space V {\displaystyle V} over a field K {\displaystyle K} that has a…

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Overview

History

Motivation

Low dimensions

Differentiable manifold

Orthogonal projections

Affine algebraic varieties

Homogeneous space

Scheme

Plücker embedding

Duality

Schubert cells

Associated measure

Orthogonal isotropic Grassmannians

Applications

Sources

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Map overview Semantic statistics

Grassmannian

Nodes180
Edges179
Triples90
Avg. degree1.99
Density0.011111
Components1

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Grassmannian

Top relations

see also · 13
Grassmannian → Affine GrassmannianGrassmann, Flag, Gauss, Given, Grassmannians, In, Isotropic GrassmannianLagrangian GrassmannianGrassmannians, Isotropic Grassmannians, K-theory, Lagrangian Grassmannians, Plücker, Schubert, Stiefel
related to Cohomology ring · 12
Grassmannian → Chern, Every, Functoriality, Gr, Grassmann, Grassmannians, In, Mapping, Similarly, The, Then, These
related to Plücker coordinates and Plücker relations · 9
Grassmannian → For, Gr, Lambda, Plücker, Since, The, The Plücker, These, To
related to Orthogonal isotropic Grassmannians · 8
Grassmannian → Cartan, Cartan's, Given, Gr, Grassmannians, Maximal, Plücker, Under
related to history · 7
Grassmannian → Gr, Grassmannians, Hermann Grassmann, Julius Plücker, Notations, Plücker, The
related to Pure mathematics · 6
Grassmannian → Another, Bethe, Gaudin, Grassmannians, Schubert, Subvarieties
related to Schubert cells · 6
Grassmannian → For, Gr, Grassmannians, Schubert, The, The Schubert
related to Low dimensions · 5
Grassmannian → For, Gr, Grassmannian Gr, In Euclidean, P2
related to Plücker embedding · 5
Grassmannian → Gr, Lambda, Supposing, The Plücker, To
related to Universal family · 5
Grassmannian → For, Gr, S-schemes, Since, The

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Important terminology

displaystyle mathbf gr space projective subset -dimensional matrix subspaces vector basis manifold times grassmannians set rank plücker subspace grassmann dots

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Grassmannianis aspace of all 2-dimensional planes containing the origin0.90text
Grassmannianis acompact Hausdorff space0.90text
Grassmannianis anon-singular algebraic variety0.90text
Grassmannianrelated to Cohomology ringEvery0.60section
Grassmannianrelated to Cohomology ringGrassmann0.60section
Grassmannianrelated to Cohomology ringGr0.60section
Grassmannianrelated to Cohomology ringMapping0.60section
Grassmannianrelated to Cohomology ringSimilarly0.60section
Grassmannianrelated to Cohomology ringThe0.60section
Grassmannianrelated to Cohomology ringGrassmannians0.60section
Grassmannianrelated to Cohomology ringChern0.60section
Grassmannianrelated to Cohomology ringIn0.60section

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    Min side: 3
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