Generalization jf Scalar Product Axioms 2004jay  Pavlov D. G.
The concept of scalar product is vital in studying basic properties of
either Euclidean or pseudoEuclidean spaces. A generalizing of a special
subclass of Finslerian spaces, that we will call the polylinear, is presented in the work. The idea of scalar polyproduct and of related fundamental metric polyform has been introduced axiomatically. The definition of different metric
parameters such as the vector length and the angle between vectors are founded on the idea. The concept of orthogonallity is also generalized. Some peculiarities of the geometry of the fourdimensional linear Finslerian space related to the algebra of commutativeassociative hypercomplex numbers, that are called Quadranumerical, are proved in the concrete polyform.
English: 

Russian: 



