Eigenvalues of a Matrix

  To calculate the eigenvalues of , we recall that the general solution for the eigenvalues of any real matrix ,

 

are given by

 

where

   

Applying these formulas to we find

and the eigenvalues for the fixed point a are

The eigenvalue is positive, and indicates an unstable direction; the eigenvalue is negative and indicates a stable direction. The fixed point a is a hyperbolic saddle.