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Jacobian matrix (of a system)

The matrix of first partial derivatives of a system's right-hand side, evaluated at a point.

For \mathbf{x}'=F(\mathbf{x}) with F=(f_1,\dots,f_n), the Jacobian matrix J at a point \mathbf{x}_0 has entry J_{ij}=\partial f_i/\partial x_j evaluated at \mathbf{x}_0 -- the best linear (matrix) approximation of F near that point.

See also

linearization (of a nonlinear system)
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