"Minors and plucker relations"의 두 판 사이의 차이
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| + | [http://www.math.msu.edu/%7Emagyar/papers/MinorIdentities.pdf http://www.math.msu.edu/~magyar/papers/MinorIdentities.pdf] | ||
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| + | <math>\Delta _{1,2}\Delta _{12,13}=\Delta _{1,3}\Delta _{12,12}+\Delta _{1,1}\Delta _{12,23}</math> | ||
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| + | # (mat = Array[Subscript[a, ##] &, {3, 3}]) // MatrixForm<br> Minors[mat] // MatrixForm<br> Minors[mat, 1] // MatrixForm<br> Minors[mat, 2] // MatrixForm<br> Minors[mat, 3] // MatrixForm | ||
| + | # Simplify[Subscript[a, 1,<br> 3]*(-Subscript[a, 1, 2] Subscript[a, 2, 1] +<br> Subscript[a, 1, 1] Subscript[a, 2, 2]) +<br> Subscript[a, 1,<br> 1]*(-Subscript[a, 1, 3] Subscript[a, 2, 2] +<br> Subscript[a, 1, 2] Subscript[a, 2, 3])] | ||
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| + | # \Delta _{12,12}\text{:=}-a_{1,2} a_{2,1}+a_{1,1} a_{2,2}\Delta _{12,23}\text{:=}-a_{1,3} a_{2,2}+a_{1,2} a_{2,3}\Delta _{1,3}\text{:=}a_{1,1}\Delta _{1,3}\text{:=}a_{1,3}\Delta _{1,3}\Delta _{12,12}+\Delta _{1,1}\Delta _{12,23} | ||
2011년 3월 9일 (수) 06:11 판
http://www.math.msu.edu/~magyar/papers/MinorIdentities.pdf
\(\Delta _{1,2}\Delta _{12,13}=\Delta _{1,3}\Delta _{12,12}+\Delta _{1,1}\Delta _{12,23}\)
- (mat = Array[Subscript[a, ##] &, {3, 3}]) // MatrixForm
Minors[mat] // MatrixForm
Minors[mat, 1] // MatrixForm
Minors[mat, 2] // MatrixForm
Minors[mat, 3] // MatrixForm - Simplify[Subscript[a, 1,
3]*(-Subscript[a, 1, 2] Subscript[a, 2, 1] +
Subscript[a, 1, 1] Subscript[a, 2, 2]) +
Subscript[a, 1,
1]*(-Subscript[a, 1, 3] Subscript[a, 2, 2] +
Subscript[a, 1, 2] Subscript[a, 2, 3])]
- \Delta _{12,12}\text{:=}-a_{1,2} a_{2,1}+a_{1,1} a_{2,2}\Delta _{12,23}\text{:=}-a_{1,3} a_{2,2}+a_{1,2} a_{2,3}\Delta _{1,3}\text{:=}a_{1,1}\Delta _{1,3}\text{:=}a_{1,3}\Delta _{1,3}\Delta _{12,12}+\Delta _{1,1}\Delta _{12,23}