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{{r|Jacobian}}

...rentiable map with a differentiable inverse. This, in turn, is true if the Jacobian matrix has nonzdero determinant (by the inverse function theorem for functi ...in this case is a matrix of four partial derivatives. Maybe you mean the Jacobian of <math>\scriptstyle\phi \circ \psi^{-1}</math>. Maybe you mean that if i

...th>h^0(K_C)=2</math>. Hence the [[canonical map]] is a double cover. The [[Jacobian variety]] of such a curve is an [[Abelian surface]]. ...ath>2^4-1=15=\mbox{binom}(6,2)</math> non-trivial 2-torsion points on this Jacobian. Moreover, if <math>p_3+p_4-H_C</math> is another (and different) 2-torsio

{{rpl|Jacobian matrix}}

The [[Jacobian]] ''J'' is the determinant

i.e. the inverse magnification factor equals the absolute value of the Jacobian determinant of the transformation described As the Jacobian determinant above approaches zero, the magnification factor becomes infinit

{{rpr|Jacobian}}

The [[Jacobian]] (Jacobi determinant) of this transformation from [[Cartesian coordinates]

...V) in the original brain can be calculated by multiplying the GMD with the Jacobian determinants of the deformations used to register the brain to the template ...metimes referred to as Tensor-based morphometry (TBM) -- is based on the [[Jacobian determinant]] of the deformation matrix.

...V) in the original brain can be calculated by multiplying the GMD with the Jacobian determinants of the deformations used to register the brain to the template ...metimes referred to as Tensor-based morphometry (TBM) -- is based on the [[Jacobian determinant]] of the deformation matrix.

*[[Jacobian matrix]]

...of the object function be known, but in some situations the derivative or Jacobian may be unavailable or prohibitively expensive to calculate. The cost can be

The weight appearing in the infinitesimal volume element d''V'' is the [[Jacobian]] (the determinant of the Jacobi matrix, which is the square root of the de

...V) in the original brain can be calculated by multiplying the GMD with the Jacobian determinants of the deformations used to register the brain to the template ...se deformations can then be used to calculate volume changes by way of the Jacobian determinant (right image).}

...V) in the original brain can be calculated by multiplying the GMD with the Jacobian determinants of the deformations used to register the brain to the template ...se deformations can then be used to calculate volume changes by way of the Jacobian determinant (right image).}

[[Jacobian matrix]],