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

Jacobian

1 9.9
A matrix of first partial derivatives of a vector function
  • noun
  • /dʒəˈkoʊbiən/
  • Specialized
: matriz jacobiana
  • In vector calculus, the Jacobian matrix is essential for transforming coordinates.

Examples

  • So the Jacobian of X&Y with respect to R and Theta is given by the following formula.

  • The second critical point gives me the Jacobian at that second point.

  • We call it the Jacobian anyway, just for short.

  • Now where is the Jacobian in all of this?

  • All right, so that's the Jacobian and one other.

  • Plus that's the Jacobian times the deviation.

  • To compute change in variables, you start with the Jacobian of the function.

  • The Jacobian provides important information about the behavior of a system near equilibrium.

Surface Forms

Jacobian singular
Jacobi plural

Morphology

Jacobian = Jacobi (opaque) = Jacobi + an

Derived from the surname 'Jacobi' plus '-an'; as an eponymous technical term it does not transparently indicate 'matrix of partial derivatives' to learners.

Etymology

Jacobian is named after the mathematician Jacobi, so it means 'of Jacobi'. In math the Jacobian is the matrix of first derivatives that tells how a function of several variables changes, which is why we call that matrix the Jacobian.