jacobian

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Definition of jacobian in English English dictionary: Used to specify certain mathematical objects named in honour of C. G. J. Jacobi
The Jacobian matrix has partial derivatives as its entries.; The determinant of such a matrix; A Jacobian matrix or its associated operator; Of or pertaining to a style of architecture and decoration in the time of James the First, of England; The determinant formed by the n<2 partial derivatives of n functions of n variables, when the derivatives of each function occupy one row of the determinant For the case of two functions f(x,y) and g(x,y) , the Jacobian J(f,g) is Sometimes written; The determinant formed by the n2 partial derivatives of n functions of n variables, when the derivatives of each function occupy one row of the determinant For the case of two functions f(x, y) and g(x, y), the Jacobian J(f, g) is sometimes also written The geostrophic advection of any scalar may be written where g is the acceleration of gravity, f the Coriolis parameter, and z the isobaric contour height; used to specify certain mathematical objects in honour of K. G. J. Jacobi; For a function the Jacobian is the n x n matrix defined as The Jacobian is used in the Newton-Raphson method and hence is very important for implicit methods It is also an indication of the coupling between components of f

jacobian

Hyphenation

Ja·co·bi·an

() After Carl Gustav Jakob Jacobi, a German mathematician of the 19th century

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