The analysis of non-autonomous systems is similar.

Analyzing the stability of autonomous vector systems

(1.12)

is more complicated. Once again, assume that is an equilibrium point and expand by Taylor's series

     .

We need a brief digression for a few definitions.

Definition: The Jacobian matrix of a vector-valued function with respect to is the matrix

(1.13)

Definition: The norm of a vector is a scalar such that

1. and if and only if y=0,
2. for any scalar and
3.