The vector space is introduced in Simple tensor algrbra I, several rules are provided in it. To reduce the abstract, we represent the vectors with the scalar coefficients and in , respectively. The composition of two vectors is expanded by,
Dot product ():
The dot product is also called scalar product or inner product under Cartesian coordinates and it provides the Euclidean magnitudes of these two vectors and the cosine of the angle between them.
Cross product ():
The cross product is also called vector product, and it represents the area of a parallelogram with the sides of these two vectors. Now, a new composition for two vectors is introduced here.
This is not a tutorial, please refer to the books for tensor algebra.