The dual space of a
vector space is the set of real valued linear functions on the
vector space. The cotangent space at a point is the dual of the tangent space at that point, and the cotangent bundle is the collection of all cotangent
spaces.. Like the tangent bundle, the cotangent bundle is again a
differentiable manifold. The Hamiltonian is a scalar on the cotangent bundle.
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vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.Scalars are often taken to be real numbers, but there are also
vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field.The operations of
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