:PROPERTIES: :ID: d02a62fb-1601-48a4-9cf2-bbb2ade26402 :mtime: 20231017013205 20231007010651 20231005014525 :ctime: 20231005014352 :END: #+title: Coordinate System (Vector Space) #+filetags: :public:project: * Defintion In a vector space, a coordinate system is a set of vectors along with an origin. * Cartesian Coordinates [[id:785f1d20-1537-4c06-9f24-d82141d2b408][Cartesian Coordinates]] have several nice properties - All axes are mutually perpendicular - All Axes emanate from a fixed origin $O$ - Axes have a fixed direction, independent of position. * Dimension The number of vectors in the coordiant system must equal the number of components of the vectors. * Span The coordinate system must span the vector space. Every vector in the vector space must be reachable from the axes * Orientation The orientation of the axes *DOES* affect the components of the vector. * Right Handed Coordinates By convention, we use right-handed coordinates.