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Keywords:
$G$-space; equivariant map; vector; scalar; biscalar
$G$-space; equivariant map; vector; scalar; biscalar
Summary:
In this note, there are determined all biscalars of a system of $s\le n$ linearly independent contravariant vectors in $n$-dimensional pseudo-Euclidean geometry of index one. The problem is resolved by finding a general solution of the functional equation $F(A{\underset{1}{\rightarrow }u},A {\underset{2}{\rightarrow }u},\dots ,A{\underset{s}{\rightarrow }u}) =( \text{sign}( \det A)) F ({\underset{1}{\rightarrow }u},{\underset{2}{\rightarrow }u},\dots ,{\underset{s}{\rightarrow }u}) $ for an arbitrary pseudo-orthogonal matrix $A$ of index one and the given vectors ${\underset{1}{\rightarrow }u}, {\underset{2}{\rightarrow }u},\dots ,{\underset{s}{\rightarrow }u}$.
References:
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