1. jacobian - Noun
2. jacobian - Adjective
Of or pertaining to a style of architecture and decoration in the time of James the First, of England.
Source: Webster's dictionaryFrom this perspective the chain rule therefore says: : or for short, : That is, the Jacobian of a composite function is the product of the Jacobians of the composed functions (evaluated at the appropriate points). Source: Internet
In this case, the above rule for Jacobian matrices is usually written as: : The chain rule for total derivatives implies a chain rule for partial derivatives. Source: Internet
A quantity called the Jacobian is useful for studying functions when both the domain and range of the function are multivariable, such as a change of variables during integration. Source: Internet
If ƒ is differentiable, this is equivalent to: : where J(x) denotes the Jacobian matrix of partial derivatives of ƒ at x and is the induced norm on the matrix. Source: Internet
Note that there may be different naming conventions, for example, IEEE P1363 -2000 standard uses "projective coordinates" to refer to what is commonly called Jacobian coordinates. Source: Internet
Other array languages may require explicit treatment of indices (for example, MATLAB ), and/or may not support higher-order functions such as the Jacobian derivative (for example, Fortran /APL). Source: Internet