Complex sentence: The form ω defined here can be shown to have the same properties as in the beginning of this section; in other words, every symplectic structure is isomorphic to one of the form "V" ⊕ "V" ∗.
Split into simpler sentences: The form ω defined here can be shown to have the same properties as in the beginning of this section. Moreover, every symplectic structure is isomorphic to one of the form "V" ⊕ "V" ∗.