- 1 Suppose We Have The Following Matrices With Matrices A And B That Do Not Depend On X U X Ea Be A Du X 1 Find D 1 (30.26 KiB) Viewed 219 times
1. Suppose we have the following matrices with matrices A and B that do not depend on x. U(x) = eA Be-A dU(x) (1) Find dx and from this show that U(x) = B + dy[A, U (y)] (2) From the result of (1), show the following. U(1) = B + [A, B] + = {A, [A, B]] + · (Hint: (1) Insert the whole right side into the U(y) part of the right side) Suppose that the following matrix is created with the matrix A, B that does not depend on x and the matrix Q(x) that depends on x. A, B satisfies [A.[= [B.LA.B]=0 ex(A+B) = eAQ(r)e (3) Using the result of (2), show the following. dQ(x) = -x[A, B]Q(x) + [B, Q(x)] dx (4) AssuminglQ.Bl= 0, find Q(x), and show that the assume "IQ.Bl=0" satisfies [BIA.B] 0. (5) From the result of (4), show the following. eA+BeeBe-[A, B] BIU Q A