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In this note all vectors and -vectors of a system of linearly independent contravariant vectors in the -dimensional pseudo-Euclidean geometry of index one are determined. The problem is resolved by finding the general solution of the functional equation with and , for an arbitrary pseudo-orthogonal matrix of index one and given vectors
There are four kinds of scalars in the -dimensional pseudo-Euclidean geometry of index one. In this note, we determine all scalars as concomitants of a system of linearly independent contravariant vectors of two so far missing types. The problem is resolved by finding the general solution of the functional equation using two homomorphisms from a group into the group of real numbers .
In this note, there are determined all biscalars of a system of linearly independent contravariant vectors in -dimensional pseudo-Euclidean geometry of index one. The problem is resolved by finding a general solution of the functional equation for an arbitrary pseudo-orthogonal matrix of index one and the given vectors .
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