{{Short description|Difference between two dimensions}} <!-- {{More citations needed|date=June 2022}} --> {{unref |date=May 2024}} In mathematics, specifically linear algebra and geometry, '''relative dimension''' is the dual notion to codimension.
In linear algebra, given a quotient map <math>V \to Q</math>, the difference dim ''V'' − dim ''Q'' is the relative dimension; this equals the dimension of the kernel.
In fiber bundles, the relative dimension of the map is the dimension of the fiber.
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.
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.
The additivity of codimension under intersection corresponds to the additivity of relative dimension in a fiber product. Just as codimension is mostly used for injective maps, relative dimension is mostly used for surjective maps.
==References== {{Reflist}}
Category:Algebraic geometry Category:Geometric topology Category:Linear algebra Category:Dimension
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