Ternary product over three-dimensional matrices
2014jrx | Lapshin A.V.  // Research Institute of Hypercomplex Systems in Geometry and Physics, Friazino, Russia, lavexander@mail.ru

The paper presents the ternary generalization of the standard algebra of matrices to the case of spatial (cubic) matrices. In addition to the definition of the ternary operation itself and to its basic properties, the multy-dimensional versions of the other conventional concepts, operations and mapping such as transposition, unit element, commutativity, associativity and others that are used in the standard algebra of matrices are constructed. The relationship between the constructed ternary operation and the algebra of polynumbersP3is discussed.

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