Symplectic group - Wikipedia: "Since all symplectic matrices have determinant 1, the symplectic group is a subgroup of the special linear group SL(2n, F).
Notational warning: What is here called Sp(2n, F) is often referred to as Sp(n, F).
More abstractly, the symplectic group can be defined as the set of linear transformations of a 2n-dimensional vector space over F that preserve a non-degenerate, skew-symmetric, bilinear form, see classical group for this definition. Such a vector space is called a symplectic vector space. The symplectic group of an abstract symplectic vector space V is also denoted Sp(V)."
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