A Necessary and Sufficient condition for all the Eigenvalues of a Real matrix *A* to have Negative Real Parts is that the equation

has as a solution where is an matrix and is a positive definite quadratic form.

**References**

Gradshteyn, I. S. and Ryzhik, I. M. *Tables of Integrals, Series, and Products, 5th ed.* San Diego, CA:
Academic Press, p. 1122, 1979.

© 1996-9

1999-05-25