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The systematic discussion of molecular symmetry is known as group theory. Group theory is a systematic way of describing the symmetry of molecules using concepts/rules borrowed from mathematics. This tag should be applied to any question which involves the theory or application of point groups, symmetry elements, or character tables.
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Decomposition of axial vector and vector representions of C4v group
Let $R$ be the orthogonal matrix corresponding to an operation in $O(3)$. If
R is a proper rotation, then both vectors $\vec{V}$ and axial vectors $\vec{A}$ are transformed in the same way
$$ \vec{V} …