Definition:Jacobian Determinant/Also presented as

Jacobian Determinant: Also presented as

A Jacobian determinant can also be written as:

$\dfrac {\map \partial {f_1, f_2, \ldots, f_n} } {\map \partial {x_1, x_2, \ldots, x_n} }$

or:

$\dfrac {\map \partial {u_1, u_2, \ldots, u_n} } {\map \partial {x_1, x_2, \ldots, x_n} }$

where:

$u_j = \map {f_j} {x_1, x_2, \ldots, x_n}$

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Jacobian or Jacobian determinant
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Jacobian
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Jacobian