Generators for symplectic matrices Every symplectic matrix has determinant , and the symplectic matrices with real entries form a subgroup of the general linear group under matrix multiplication since being symplectic is a property stable under matrix multiplication. Topologically, this symplectic group is a connected noncompact real Lie group of real dimension , and is denoted . The symplectic group can be defined as the set of linear transformations that preserve the symplectic form of a real symplectic vector space.
Generators for symplectic matrices Every symplectic matrix has determinant , and the symplectic matrices with real entries form a subgroup of the general linear group under matrix multiplicatio,n since being symplectic is a property stable under matrix multiplication. Topologically, this symplectic group is a connected noncompact real Lie group of real dimension , and is denoted . The symplectic group can be defined as the set of :linear transformations that preserve the symplectic form of a real symplectic vector space.