• Let X_(H) be the n-dimensional spectral
subspace corresponding to eigenvalues in Re s <0:
•
• where X1, X2 Î Cn´n (X1 and X2 can be
chosen to be real matrices.) If X1 is
nonsingular, define
•X:=Ric(H)= X2 X1-1: dom(Ric) Ì R2n´2n ® R2n´2n
• where dom(Ric) consists of all H matrices such that
v H has no eigenvalues on
the imaginary axis
v are
complementary (or X1 is nonsingular.)
v Then X is a solution of the ARE. (see next theorem)
v>>[X1,X2] = ric_schr(H), X = X2/X1