"Grassmannian variety"의 두 판 사이의 차이
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| − | + | <h5>Plücker embedding</h5> | |
<math>N=\binom{n}{k}</math> | <math>N=\binom{n}{k}</math> | ||
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<math>P_{I}(A)</math> = determinant of submatrix of A with column set I | <math>P_{I}(A)</math> = determinant of submatrix of A with column set I | ||
| − | + | <math>\begin{array}{l} \Delta _{1,2}=a_{1,1} a_{2,2}-a_{1,2} a_{2,1} \\ \Delta _{1,3}=a_{1,1} a_{2,3}-a_{1,3} a_{2,1} \\ \Delta _{1,4}=a_{1,1} a_{2,4}-a_{1,4} a_{2,1} \\ \Delta _{2,3}=a_{1,2} a_{2,3}-a_{1,3} a_{2,2} \\ \Delta _{2,4}=a_{1,2} a_{2,4}-a_{1,4} a_{2,2} \\ \Delta _{3,4}=a_{1,3} a_{2,4}-a_{1,4} a_{2,3} \end{array}</math> | |
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2012년 8월 1일 (수) 18:53 판
introduction
\(Gr_{kn}(\mathbb{R})=GL_k\Mat(k,n)\)
Plücker embedding
\(N=\binom{n}{k}\)
\(Gr_{kn}(\mathbb{R}) \to \mathbb{P}^{N-1}\)
\(P_{I}(A)\) = determinant of submatrix of A with column set I
\(\begin{array}{l} \Delta _{1,2}=a_{1,1} a_{2,2}-a_{1,2} a_{2,1} \\ \Delta _{1,3}=a_{1,1} a_{2,3}-a_{1,3} a_{2,1} \\ \Delta _{1,4}=a_{1,1} a_{2,4}-a_{1,4} a_{2,1} \\ \Delta _{2,3}=a_{1,2} a_{2,3}-a_{1,3} a_{2,2} \\ \Delta _{2,4}=a_{1,2} a_{2,4}-a_{1,4} a_{2,2} \\ \Delta _{3,4}=a_{1,3} a_{2,4}-a_{1,4} a_{2,3} \end{array}\)
example Gr(2,4)