Math 2.0

Real functions Concept

Jacobian determinant

Builds on Jacobian matrix

Summary

The Jacobian determinant of a map from an open subset of ℝn\mathbb{R}^n to ℝn\mathbb{R}^n at a point is the determinant of its Jacobian matrix there. Its absolute value is the factor by which the map scales small volumes near the point. Its sign tells whether the map keeps or reverses orientation.

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Euclidean space, object, no evidence levelEuclidean spaceobjectFunction, concept, no evidence levelFunctionconceptTotal derivative, concept, no evidence levelTotal derivativeconceptFunction of several variables, concept, no evidence levelFunction of several v…conceptPartial derivative, concept, no evidence levelPartial derivativeconceptJacobian matrix, concept, no evidence levelJacobian matrixconceptJacobian determinant, concept, no evidence levelJacobian determinantconcept
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
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  1. Euclidean space object
  2. Function concept
  3. Total derivative concept
  4. Function of several variables concept
  5. Partial derivative concept
  6. Jacobian matrix concept
  7. Jacobian determinant concept

Where this leads

6 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant, Jacobian determinant
About this page
Tag0ZCSMYHTBP
URIm2://0ZCSMYHTBP
Aliasesjacobian-of-a-map
Kindconcept
WritingW0 stub
MSC26B10
UsesJacobian matrix

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