This leads to expressing the basic

Jacobian matrix (1) for the total number of fingers.

Jacobian matrix As in the classical case, the

Jacobian matrix of H(Z, y) with respect to y, denoted by [partial derivative]H/[partial derivative]y is the matrix whose entries are [partial derivative][H.

It is also possible to compute gradients (a special case of Jacobians) of structured computations by exposing the sparsity in an associated extended

Jacobian matrix [Coleman and Jonsson 1999].

A second concept of interaction strength, advanced by May (1973), are the elements in the

Jacobian matrix near equilibrium.

where [J] is the

Jacobian matrix, [[phi]] is a column vector containing the solution at the iteration indicated by the super index and [F[([phi]).

When the forward model is solved, the sensitivity map, also known as

Jacobian matrix, can then be defined.

And we also can derive the

Jacobian matrix from the velocity equation to judge the singular position.

is the joint variables vector and J the

Jacobian matrix (Yoshikawa, 1985).

For the applications that we are interested in, n is usually large, and in this case, the algorithm has three expensive operations: the evaluation of F(x), the construction of the

Jacobian matrix, and the solution of the Jacobian system.

where, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], with J as the Phantom

jacobian matrix.

n] to (1) is singular if the

Jacobian matrix at z, [D.

Model food chains of varying lengths and complexities, as represented by the well-known

Jacobian matrix of linearized effects at equilibrium densities, were then examined.