In mathematics, specifically linear algebra and geometry, relative dimension is the dual notion to codimension.
In linear algebra, given a quotient map, 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 of codimension k dualizes to yield a quotient map 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.
Famous quotes containing the words relative and/or dimension:
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—Charles Sanders Peirce (1839–1914)
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—Shoshana Zuboff (b. 1951)