Convex Set Definition Finite-Dimensional Vector Space Definition Exponential Law for a Single Matrix Geometry Atiyah Guillemin Sternberg Convexity Theorem Geometry Naturality of the Lie Group Exponential Geometry Local Description of Sections of a Vector Bundle Geometry Naturality of Chern-Weil Forms Geometry Pullback of a Smooth Vector Bundle Is a Smooth Vector Bundle Geometry First Chern Class Classification of Complex Line Bundles Geometry Hodge Symmetry for Compact Kähler Manifolds Geometry Geometry Area