This is homework assignment 6, due on Friday, 27th September.

Problem: Show that Eq. 9.55 of the text MJM^T = J, implies that the fundamental Poisson brackets are invariant under the canonical transformation, given my matrix M. Do this by following these steps.
(1) First calculate the ijth element of the LHS. 
(2) Consider four separate cases (i) i < n+1, j < n+1 (ii) i > n, j < n+1 (iii) i > n, j > n (iv) i < n+1, j > n. 
(3) For each case show that it is either zero or a Poisson bracket. 
(4) Then equate the non-zero terms with the corresponding ijth element of the RHS. 
(5) Comment on what these equalities together imply. 

Solutions and Grades.