題組內容

8.(10%) Consider the following Lyapunov equation
 XA+ATX+Q=0
 where A is a (n-dimensional) real square matrix, and X, Q are real symmetric matrices. 

(a) (5%) Suppose all eigenvalues of A have negative real parts. Show that X =63084478514fe.jpgdτ a solution to the Lyapunov equation.