Grassmannian variety

introduction

• minors and plucker relations

 

\definition

 

real Grassmannian

 

\(Gr_{kn}(\mathbb{R}) = \{V\subset \mathbb{R}^n | \dim V = k\}\)

 

can represent element by full rank k x n matrix

 

\(Gr_{kn}(\mathbb{R})=GL_k\Mat(k,n)\)

 

Plucker embedding

 

\(Gr_{kn}(\mathbb{R}) \to \mathbb{P}^{n-1}\)

 

\(P_{I}(A)\) = determinant of submatrix of A  with column set I

 

 

 

 

 

 

expositions

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