On the Symplectic Eigenvalues of Positive Definite Matrices

Аннотация

A simple proof of Williamson’s theorem is given. This theorem states that a real symmetric positive definite matrix A of even order can be brought to diagonal form Λ by a symplectic congruence transformation. The diagonal entries of Λ are called symplectic eigenvalues of A. The problem of calculating these values is also discussed.