Plücker coordinates: Difference between revisions

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[[File:Plucker_embedding.png|thumb|600px|right|Schematic illustration of the Plücker embedding. Linear subspaces of <math>\mathbb{R}^n</math> (here lines) get mapped to points on a quadric surface in projective space.]]

In [[exterior algebra]] applied to [[regular temperament theory]], '''Plücker coordinates''' (also known as the [[wedgie]]) are a way to assign coordinates to abstract temperaments, by viewing them as elements of some projective space.

In [[exterior algebra]] applied to [[regular temperament theory]], '''Plücker coordinates''' (also known as the '''wedgie''') are a way to assign coordinates to abstract temperaments, by viewing them as elements of some projective space.

The usual way to write down an abstract temperament is via its mapping matrix, but Plücker coordinates give us a unique description that is useful for some calculations.

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Since for any decent temperament this angle will be extremely small, we can take <math>\sin (\theta) \approx \theta</math>.

== See also ==

* [[Wedgie supplement]] - Supplementary page going over additional information on wedgies

* [[Exterior algebra]] - exterior product, which produces wedgies

* [[Interior product]] - interior product, dual of the exterior product

* [[Hodge dual]] - acts on wedgies

[[Category:Exterior algebra]]

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-{{Expert}}
+{{Expert|Wedgie}}
 [[File:Plucker_embedding.png|thumb|600px|right|Schematic illustration of the Plücker embedding. Linear subspaces of <math>\mathbb{R}^n</math> (here lines) get mapped to points on a quadric surface in projective space.]]
 {{Wikipedia|Plücker embedding}}
-In [[exterior algebra]] applied to [[regular temperament theory]], '''Plücker coordinates''' (also known as the [[wedgie]]) are a way to assign coordinates to abstract temperaments, by viewing them as elements of some projective space.
+In [[exterior algebra]] applied to [[regular temperament theory]], '''Plücker coordinates''' (also known as the '''wedgie''') are a way to assign coordinates to abstract temperaments, by viewing them as elements of some projective space.
 The usual way to write down an abstract temperament is via its mapping matrix, but Plücker coordinates give us a unique description that is useful for some calculations.
@@ Line 136: / Line 136: @@
 Since for any decent temperament this angle will be extremely small, we can take <math>\sin (\theta) \approx \theta</math>.
+== See also ==
+* [[Wedgie supplement]] - Supplementary page going over additional information on wedgies
+* [[Exterior algebra]] - exterior product, which produces wedgies
+* [[Interior product]] - interior product, dual of the exterior product
+* [[Hodge dual]] - acts on wedgies
 [[Category:Exterior algebra]]