Symplectic Linear Algebra

A symplectic structure on a smooth manifold is defined by assigning a symplectic form to the tangent space at each point of the manifold, with additional property which we will see in the next chapter. Considering tangent spaces as vector spaces motivates us to study first about symplectic linear algebra. Hence, in this chapter we study symplectic forms over vector spaces, and we see properties, examples, and more definitions in the linear world. Symplectic linear algebra by itself is an interesting source for a lot of investigations.