Vectors, Dual Vectors, and Tensors

1. Vectors Tangent Space (T_p): The set of all possible vectors located at each point p in spacetime Vector Space: A collection of vectors that can be added together and multiplied by real numbers in a linear way; Vector Field: A set of vectors with exactly one at each point in spacetime Tangent Bundle: 2n-dimensional manifold which assembles the set of all the tangent spaces of an n-dimensional manifold Basis: Any set of vectors which both spans the vector space and is linearlly independent; Ta...