A **symplectic matrix** is a special type of square matrix that preserves a symplectic form. Symplectic matrices are used primarily in the context of symplectic geometry and Hamiltonian mechanics.
Articles by others on the same topic
An invertible real matrix preserving the standard symplectic form. With , it satisfies , equivalently . The first identity describes preservation of the form; the second describes preservation of coordinate Poisson brackets.
