Question

Need help to understand this. Please expalin how did they get each steps. specially the underlined one. How did it came and then third step (-I_n J^-1.) Also what is symplectic matrix. What is the value of AA^{T ?}

s symplectic thanM

Answer 1

a symplectic matrix is a 2n x2n matrix M with real entries that satisfies the condition where MT denotes the transpose of Mand J is a fixed 2nx 2n nonsingular,skew- symmetric matrix given M is symplectic matrix ョ a fixed 2n× 2n non singular, skew-symm etric m atrix J, J = so that is non singular, skew-symmetric matrix, J we need to prove M is symplectic matrix consider (MTYJMT-MJMT using Associative property Note that J2-1 MM-J-1 -1