Relative Dimension
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High Quality Content by WIKIPEDIA articles! In mathematics, specifically linear algebra and geometry, relative dimension is the dual notion to codimension.In linear algebra, given a quotient map V to Q, 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 V to W of codimension ...
High Quality Content by WIKIPEDIA articles! In mathematics, specifically linear algebra and geometry, relative dimension is the dual notion to codimension.In linear algebra, given a quotient map V to Q, 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 V to W of codimension k dualizes to yield a quotient map W^ to V^ of relative dimension k, and conversely. The additivity of codimension under intersection corresponds to the additivity of relative dimension in a fiber product.
