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codimension

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In mathematics, codimension is a basic geometric idea that applies to subspaces in vector spaces, to submanifolds in manifolds, and suitable subsets of algebraic varieties.

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Instance of
invariant
Subclass of
difference
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facet of
dimension
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Encyclopedic overview

6 sections
Contents
  • Definition
  • Additivity of codimension and dimension counting
  • Dual interpretation
  • In geometric topology
  • See also
  • References

In mathematics, codimension is a basic geometric idea that applies to subspaces in vector spaces, to submanifolds in manifolds, and suitable subsets of algebraic varieties.

For affine and projective algebraic varieties, the codimension equals the height of the defining ideal. For this reason, the height of an ideal is often called its codimension.

Excerpted from Wikipedia’s “codimension” article, available under the CC BY-SA 4.0 licence.