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| | I'm Miles and I live in a seaside city in northern Netherlands, Tilburg. I'm 28 and I'm will soon finish my study at Biology.<br><br>Feel free to surf to my site - [http://sumithdias.com/?p=36 pussy riot a punk prayer online] |
| In [[mathematics]], specifically [[linear algebra]] and [[geometry]], '''relative dimension''' is the dual notion to [[codimension]].
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| In linear algebra, given a [[quotient space (linear algebra)|quotient map]] <math>V \to Q</math>, the difference dim ''V'' − dim ''Q'' is the relative dimension; this equals the dimension of the kernel.
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| In [[fiber bundle]]s, the relative dimension of the map is the dimension of the fiber.
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| More abstractly, the codimension of a map is the dimension of the [[cokernel]], while the relative dimension of a map is the dimension of the [[Kernel (algebra)|kernel]].
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| These are dual in that the inclusion of a subspace <math>V \to W</math> of codimension ''k'' dualizes to yield a quotient map <math>W^* \to V^*</math> of relative dimension ''k'', and conversely.
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| The additivity of codimension under intersection corresponds to the additivity of relative dimension in a [[fiber product]].
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| Just as codimension is mostly used for [[injective]] maps, relative dimension is mostly used for [[surjective]] maps.
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| [[Category:Algebraic geometry]]
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| [[Category:Geometric topology]]
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| [[Category:Linear algebra]]
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| [[Category:Dimension]]
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| {{geometry-stub}}
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Latest revision as of 20:31, 15 April 2014
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