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Glite Dictionary
📐 About the matrix 🧮 A matrix 🔢 A determinant 📊 An algebraic object
Jacobian

Jacobian

1 9.9
A number from a matrix of first partial derivatives showing area or volume change
  • noun
  • /dʒəˈkoʊbiən/
  • Specialized
: jacobiano
  • This parallel parallelotope goes by G into this one, and its volume is the Jacobian, which is the determinant of G.

Examples

  • So the determinant of the Jacobian is independent of the frame.

  • In calculus, the Jacobian helps us understand how functions change in multidimensional space.

  • The determinant of the Jacobian is independent of the frame.

  • This parallel parallelotope goes by G into this one, and its volume is the Jacobian, which is the determinant of G.

Synonyms

determinant
vsJacobian
  • Specialized
1 9.5

A number calculated from a square grid of numbers that helps solve many equations

is the specific value used to measure area or volume change under transformations

Surface Forms

Jacobian singular
Jacobi plural

Morphology

Jacobian = Jacobi (opaque) = Jacobi + an

Eponymous derivation from 'Jacobi' + '-an'; the name-based formation does not transparently indicate the specific concept of a determinant measuring area/volume change.

Etymology

Jacobian comes from the name of the mathematician Jacobi, so it means 'of Jacobi'. In calculus the Jacobian (the determinant of that matrix) measures how much an area or volume stretches or shrinks under a change, which explains its modern use.