|
The name paravector is used for the sum of a scalar and a vector in any Clifford algebra (Clifford algebra is also known as geometric algebra in the physics community.) This name was given by J. G. Maks, Doctoral Dissertation, Technische Universiteit Delft (Netherlands), 1989. The complete algebra of paravectors along with corresponding higher grade generalizations, all in the context of the Euclidean space of three dimensions, is an alternative approach to the spacetime algebra (STA) introduced by David Hestenes. This alternative algebra is called algebra of physical space (APS). ==Fundamental axiom== For Euclidean spaces, the fundamental axiom indicates that the product of a vector with itself is the scalar value of the length squared (positive) : Writing : and introducing this into the expression of the fundamental axiom : we get the following expression after appealing to the fundamental axiom again : which allows to identify the scalar product of two vectors as : As an important consequence we conclude that two orthogonal vectors (with zero scalar product) anticommute : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「paravector」の詳細全文を読む スポンサード リンク
|