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The seco nd orthogonalit y conditions are used to provide a conc ise proof of the theore m that two rot ation ma tri ces co nnec ted by an orthogona l s imil a rit y tra nsformation ha ve th e sa me angJes of rotations . This th eo re m is di scussed in the cont ex t of it s a ppli cability to the proble m of deco mpos ing the rea l ort hogo na l group 0(3) into its c lasses of co njugate e le ments.

The second orthogonality conditions in the theory of proper and improper rotations .III. The conjugacy theorem