Block perturbation of symplectic matrices in Williamson's theorem

Gajendra Babu, Hemant K. Mishra

Williamson's theorem states that for any $2n\times 2n$ real positive definite matrix $A$, there exists a $2n\times 2n$ real symplectic matrix $S$ such that $S^{T}AS=D\oplus D$, wh…